How to overcome fear of annihilation in meditation and why is it not included in list of hindrances to meditation?

"As the mind knows that total emptiness will be the end of 'mind' or 'ego' I think the fear springs from that idea." Then simply let go of such ideas and ways of thinking about being or not-being (as both is wrong thinging). Just 'this isn't real, lasting, worthy to hold on it, make it mine.' The hindrance is simply doubt, and possible caused by neither listen to the good teaching or with wrong attention (e.g. lack of good association). What should be feared to get lost if of no worth and the Buddha didn't thought of others to just get lost. Does this arising thought, idea last? Real? Then, go on for heartwood beyond it, just knowing 'oh, this thought'.

The Visuddhimagga or the Path of Purification by Ven. Buddhaghosa is useful for this purpose. Please see "Path of Purification (Visuddhimagga)", translated from Pali by Ven. Ñāṇamoli. It's a classic manual of Buddhist doctrine and meditation written in approximately the 5th century CE, and is considered the most important Theravada text outside the Pali Canon and its traditional commentaries.

It talks about the eight knowledges of insight:

Now, insight reaches its culmination with the eight knowledges, and knowledge in conformity with truth is ninth; these are what is called purification by knowledge and vision of the way.The eight should be understood as follows: (1) knowledge of contemplation of rise and fall, which is insight free from imperfections and steady on its course,(2) knowledge of contemplation of dissolution, (3) knowledge of appearance as terror, (4) knowledge of contemplation of danger, (5) knowledge of contemplation of dispassion, (6) knowledge of desire for deliverance, (7) knowledge of contemplation of reflection, and (8) knowledge of equanimity about formations.

“Knowledge in conformity with truth as ninth” is a term for conformity.So one who wants to perfect this should make these kinds of knowledge his task, starting with knowledge of rise and fall free from imperfections.

The description of (3) knowledge of appearance as terror:

As he repeats, develops and cultivates in this way the contemplation of dissolution, the object of which is cessation consisting in the destruction, fall and breakup of all formations, then formations classed according to all kinds of becoming, generation, destiny, station, or abode of beings, appear to him in the form of a great terror, as lions, tigers, leopards, bears, hyenas, spirits, ogres, fierce bulls, savage dogs, rut-maddened wild elephants, hideous venomous serpents,thunderbolts, charnel grounds, battlefields, flaming coal pits, etc., appear to a timid man who wants to live in peace. When he sees how past formations have ceased, present ones are ceasing, and those to be generated in the future will cease in just the same way, then what is called knowledge of appearance as terror arises in him at that stage. ...

But does the knowledge of appearance as terror [itself] fear or does it not fear? It does not fear. For it is simply the mere judgment that past formations have ceased, present ones are ceasing, and future ones will cease. Just as a man with eyes looking at three charcoal pits at a city gate is not himself afraid, since he only forms the mere judgment that all who fall into them will suffer no little pain;—or just as when a man with eyes looks at three spikes set in a row, an acacia spike, an iron spike, and a gold spike, he is not himself afraid, since he only forms the mere judgment that all who fall on these spikes will suffer no little pain;—so too the knowledge of appearance as terror does not itself fear; it only forms the mere judgment that in the three kinds of becoming, which resemble the three charcoal pits and the three spikes, past formations have ceased, present ones are ceasing, and future ones will cease.

The description of (4) knowledge of contemplation of danger:

As he repeats, develops and cultivates the knowledge of appearance as terror he finds no asylum, no shelter, no place to go to, no refuge in any kind of becoming, generation, destiny, station, or abode. In all the kinds of becoming,generation, destiny, station, and abode there is not a single formation that he can place his hopes in or hold on to. The three kinds of becoming appear like charcoal pits full of glowing coals, the four primary elements like hideous venomous snakes (S IV 174), the five aggregates like murderers with raised weapons (S IV174), the six internal bases like an empty village, the six external bases like village-raiding robbers (S IV 174–75), the seven stations of consciousness and the nine abodes of beings as though burning, blazing and glowing with the eleven fires (see S IV 19), and all formations appear as a huge mass of dangers destitute of satisfaction or substance, like a tumour, a disease, a dart, a calamity,an affliction (see M I 436). How?

They appear as a forest thicket of seemingly pleasant aspect but infested with wild beasts, a cave full of tigers, water haunted by monsters and ogres, an enemy with raised sword, poisoned food, a road beset by robbers, a burning coal, a battlefield between contending armies appear to a timid man who wants to live in peace. And just as that man is frightened and horrified and his hair stands up when he comes upon a thicket infested by wild beasts, etc., and he sees it as nothing but danger, so too when all formations have appeared as a terror by contemplation of dissolution, this meditator sees them as utterly destitute of any core or any satisfaction and as nothing but danger.

Apparently, this will transition into a knowledge of peace:

“He contemplates as suffering
Arising, occurrence, and the sign,
Accumulation, rebirth-linking —
And this his knowledge is of danger.

“He contemplates as bliss no arising,
And no occurrence, and no sign,
No accumulation, no rebirth-linking —
And this his knowledge is of peace.

“This knowledge about danger has
Five sources for its origin;
Knowledge of peace has also five —
Ten knowledges he understands.

Knowledge of the state of peace is this: “Non-arising is safety,” etc.: this, however, should be understood as said for the purpose of showing the opposite kind of knowledge to knowledge of danger. Or when it is stated in this way, that there is safety without terror and free from danger, it is for the purpose of comforting those who are upset in their hearts by seeing danger through appearance as terror. Or else, when arising, etc., have clearly appeared to a man as terror, his mind inclines towards their opposites, and so this is said for the purpose of showing the advantages in the knowledge of danger established by the appearance as terror.

So, the mind first sees the terror of the inevitability of the cessation of phenomena, and then experiences danger when it realizes that there is no place to cling to for safety from the inevitability of the cessation of phenomena. Finally, it accepts this situation, and sees non-arising etc. as safety.

Is fear not one of the five hindrances?

Well, if the terror of the inevitability of the cessation of phenomena, or the danger of no place to cling to for safety from cessation, hinders one from progress due to fear, then this falls under the hindrance of doubt or uncertainty (vicikicchā), in my opinion, because the mind is doubtful and lacks conviction and trust, on whether it is the right way forward.

The same text states:

It is without wish to cure (vigatá cikicchá), thus it is uncertainty (vicikicchá). It has the characteristic of doubt. Its function is to waver. It is manifested as indecisiveness, or it is manifested as taking various sides. Its proximate cause is unwise attention. It should be regarded as obstructive of theory (see XVII.52).

In a way, fear of annihilation is part of the five hindrances, for example:

• attachment to/desire for the continuation of sensory perception (i.e. to the physical body)
• resentment/bitterness toward mortality
• doubt in the concept of Anattā

Since individualism is a central tenet of Western civilization, it can be especially hard to anticipate 2 annihilations: the inevitable death of the body and the annihilation of self (the latter in Zen is called "the Great Death") as a necessary step in attainment.

In addition, in Western culture we tend to "hide" death as much as possible, compared to Asian cultures. For example, there is a long tradition of monks meditating around a deceased person in Asia - not to mention the tradition of Tibetan sky burials. You might say we "push death away" much more in Western culture.

As a consequence, we perhaps tend to "push Anattā away" in the same way we avoid being confronted with physical death (consciously or culturally). I struggled with this my "self", until my teacher urged me to really mentally dive into what really discomforted me regarding this idea - and that's all it turned out to be in my case: the imaginings of what the actual event of self-annihilation would be like. Like what most people fear about physical death is not death itself, but the way it will come, I had formed the most terrifying scenarios in my head what this "dying process of the self" would be like. I would almost call it "spiritual hypochondria" in my case.

Needless to say, all these imagined scenarios were completely absent from the initial glimpse of the actual experience (in my case through Kōan practice). But I did need that initial push from my teacher to dive into my extreme discomfort of the idea to get there.

Hope this helps.