When you see The Light (according to textual sources)

I don't think it's described as a "feeling", nor even exactly as a "sight", in the Pali suttas.

The most famous description might, I guess, be from Ariyapariyesana Sutta: The Noble Search (MN 26), translated as follows, describing the Buddha's own enlightenment:

"In search of what might be skillful, seeking the unexcelled state of sublime peace, I wandered by stages in the Magadhan country and came to the military town of Uruvela. There I saw some delightful countryside, with an inspiring forest grove, a clear-flowing river with fine, delightful banks, and villages for alms-going on all sides. The thought occurred to me: 'How delightful is this countryside, with its inspiring forest grove, clear-flowing river with fine, delightful banks, and villages for alms-going on all sides. This is just right for the exertion of a clansman intent on exertion.' So I sat down right there, thinking, 'This is just right for exertion.'

"Then, monks, being subject myself to birth, seeing the drawbacks of birth, seeking the unborn, unexcelled rest from the yoke, Unbinding, I reached the unborn, unexcelled rest from the yoke: Unbinding. Being subject myself to aging... illness... death... sorrow... defilement, seeing the drawbacks of aging... illness... death... sorrow... defilement, seeking the aging-less, illness-less, deathless, sorrow-less, unexcelled rest from the yoke, Unbinding, I reached the aging-less, illness-less, deathless, sorrow-less, unexcelled rest from the yoke: Unbinding. Knowledge & vision arose in me: 'Unprovoked is my release. This is the last birth. There is now no further becoming.'

"Then the thought occurred to me, 'This Dhamma that I have attained is deep, hard to see, hard to realize, peaceful, refined, beyond the scope of conjecture, subtle, to-be-experienced by the wise. [3] But this generation delights in attachment, is excited by attachment, enjoys attachment. For a generation delighting in attachment, excited by attachment, enjoying attachment, this/that conditionality & dependent co-arising are hard to see. This state, too, is hard to see: the resolution of all fabrications, the relinquishment of all acquisitions, the ending of craving; dispassion; cessation; Unbinding.

So it's described as an arising of "knowledge and vision".

This version is very slightly different:

Knowledge and vision arose in me:
Ñāṇañca pana me dassanaṃ udapādi:

‘My freedom is unshakable; this is my last rebirth; now there are no more future lives.’
‘akuppā me vimutti, ayamantimā jāti, natthi dāni punabbhavo’ti.

Maybe that (difference between "unprovoked" and "unshakeable") is in how akuppā is translated.

See also:

• Definitions for dassana
• Definitions for ñāṇa

The definition for dassana includes,

in combination ñāṇa-dassana either “knowing & seeing,” or perhaps “the insight arising from knowledge,” perfect knowledge, realization of the truth, wisdom

... so perhaps not literally "sight", but rather "insight".

("Right View" i.e. samma ditthi isn't mentioned here, but that's another example of the dhamma using a word for sight, i.e. view, in a not-quite literal way -- to mean something like "insight" or something seen or formed by the mind, rather than seen by the eye).

There's a more detailed description given in this formula: Knowledge of the destruction of the āsavas

I won't quote it here because it's better to see the original page (i.e. follow the hyperlink). All the words on that page are linked to dictionary definitions, if you hover over the word with a mouse.

Note that "enlightenment" and "see the light" are Western or European, English-language, expressions or idioms. Wikipedia's Enlightenment in Buddhism says,

The English term enlightenment is the western translation of the term bodhi, "awakening", which was popularised in the Western world through the 19th century translations of Max Müller. It has the western connotation of a sudden insight into a transcendental truth.

The term is also being used to translate several other Buddhist terms and concepts used to denote insight (prajna, kensho and satori); knowledge (vidhya); the "blowing out" (Nirvana) of disturbing emotions and desires and the subsequent freedom or release (vimutti); and the attainment of Buddhahood, as exemplified by Gautama Buddha.

What exactly constituted the Buddha's awakening is unknown. It may probably have involved the knowledge that liberation was attained by the combination of mindfulness and dhyāna, applied to the understanding of the arising and ceasing of craving. The relation between dhyana and insight is a core problem in the study of Buddhism, and is one of the fundamentals of Buddhist practice.

I expect there are other descriptions, in the suttas, and in other sources (other than the suttas, perhaps other schools/traditions of Buddhism); I think though this is the most famous description in the suttas.

And there are other descriptions, of what enlightenment is; of what the Tathagata is or isn't like, after enlightenment; and of the path[s] to enlightenment.