Other than physical form which characteristics define a woman?

In the Sabbasava Sutta, Buddha described questions regarding identity as "inappropriate attention":

When a monk attends inappropriately, unarisen fermentations arise, and arisen fermentations increase.

...

"This is how he attends inappropriately: 'Was I in the past? Was I not in the past? What was I in the past? How was I in the past? Having been what, what was I in the past? Shall I be in the future? Shall I not be in the future? What shall I be in the future? How shall I be in the future? Having been what, what shall I be in the future?' Or else he is inwardly perplexed about the immediate present: 'Am I? Am I not? What am I? How am I? Where has this being come from? Where is it bound?'

"As he attends inappropriately in this way, one of six kinds of view arises in him: The view I have a self arises in him as true & established, or the view I have no self... or the view It is precisely by means of self that I perceive self... or the view It is precisely by means of self that I perceive not-self... or the view It is precisely by means of not-self that I perceive self arises in him as true & established, or else he has a view like this: This very self of mine — the knower that is sensitive here & there to the ripening of good & bad actions — is the self of mine that is constant, everlasting, eternal, not subject to change, and will stay just as it is for eternity. This is called a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. Bound by a fetter of views, the uninstructed run-of-the-mill person is not freed from birth, aging, & death, from sorrow, lamentation, pain, distress, & despair. He is not freed, I tell you, from suffering & stress.

https://www.accesstoinsight.org/tipitaka/mn/mn.002.than.html

The Pali scriptures refer to the 'faculty of femininity' ('itthindriya'), as follows:

Mendicants, there are these three faculties.What three? The faculties of femininity (itthindriya), masculinity (purisindriya) and life (jīvitindriya).

SN 48.22

Thus, it appears the biological aggregate/faculty of form may possibly be one way to define a "woman" (itthi). However, it appears such a biological definition is not necessarily "identity" ("jati").

SN 12.2 defines "identity" ("jati") as follows:

Yā tesaṃ tesaṃ sattānaṃ tamhi tamhi sattanikāye jāti sañjāti okkanti abhinibbatti khandhānaṃ pātubhāvo āyatanānaṃ paṭilābho

Here, SN 12.2 (& also MN 98) explains "identity" ("jati") is produced (abhinibbatti) from how both physical & mental aggregates are manifested & used (khandhānaṃ pātubhāvo) and from what sense objects are sought & taken possession of (āyatanānaṃ paṭilābho).

Therefore, the following suttas AN 6.52 & AN 7.51 below describe other characteristics which define a woman. In other words, AN 6.52 & AN 7.51, below, provide descriptions the manifestation & use of aggregates ('faculties', 'gestures', 'manners', 'poise', 'desires', 'voice', 'charms', 'delight', 'excitement', 'attending outwardly', etc) and the seeking/taking possession of sense objects (such as 'a man', 'children', 'adornments', etc) which may possibly define the category of beings (sattanikāye) called "women".

Itthī kho, brāhmaṇa, purisādhippāyā alaṅkārūpavicārā puttādhiṭṭhānā asapattībhinivesā issariyapariyosānā ti

A man, O brahmin, is a woman’s aim, her quest is for adornments, her mainstay is sons, her desire is to be without a co-wife and her ideal is domination. (Nyanaponika)

A man, brahmin, is the aim of women; their quest is for adornments; sons are their support; they on intent on being without a rival; and their final goal is authority. (Bodhi)

Women have a man as their ambition. They’re preoccupied with adornments. They’re dedicated to their children. They insist on being without a co-wife. Their ultimate goal is authority. (Sujato)

AN 6.52

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The Blessed One said: “A woman attends (manasi karoti) inwardly to her feminine faculties (itthindriya), her feminine gestures, her feminine manners, feminine poise, feminine desires, feminine voice, feminine charms. She is excited by that, delighted by that. Being excited & delighted by that, she attends outwardly to masculine faculties, masculine gestures, masculine manners, masculine poise, masculine desires, masculine voices, masculine charms. She is excited by that, delighted by that. Being excited & delighted by that, she wants to be bonded to what is outside her, wants whatever pleasure & happiness that arise based on that bond. Delighting, caught up in her femininity, a woman goes into bondage with reference to men. This is how a woman does not transcend (nātivattati) her femininity.

AN 7.51

The above said, an enlightened bhikkhuni (Buddhist nun) that does not manifest/use/possess aggregates & sense objects in the above described ways appears to not have the identity (jati) of "a woman", as follows:

What does womanhood matter at all. When the mind is concentrated well. When knowledge flows on steadily. As one sees correctly into Dhamma.

One to whom it might occur, 'I'm a woman' or 'I'm a man' Or 'I'm anything at all' — Is fit for Mara to address.

SN 5.2

However, AN 7.51 does contain the phrase: "This is how a woman transcends her femininity. Evaṃ kho, bhikkhave, itthī itthattaṃ ativattati".

Therefore, it appears the 'faculty of femininity' ('itthindriya') or form aggregate may possibly generically define a "woman" however such "femininity" can be "transcended" ("ativattati") by not attending to it (na manasi karoti), by not manifesting it (na khandhānaṃ pātubhāvo) & by not identifying with it (anabhiratā).

And how does one become unbound?

Kathañca, bhikkhave, visaṃyogo hoti?

A woman doesn’t focus on her own femininity:

Itthī, bhikkhave, ajjhattaṃ itthindriyaṃ na manasi karoti—

her feminine moves, feminine appearance, feminine ways, feminine desires, feminine voice, and feminine adornment.

itthikuttaṃ itthākappaṃ itthividhaṃ itthicchandaṃ itthissaraṃ itthālaṅkāraṃ.

She isn’t stimulated by this and takes no pleasure in it.

Sā tattha na rajjati, sā tatra nābhiramati.

So she doesn’t focus on the masculinity of others:

Sā tattha arattā tatra anabhiratā bahiddhā purisindriyaṃ na manasi karoti—

masculine moves, masculine appearance, masculine ways, masculine desires, masculine voice, and masculine adornment.

purisakuttaṃ purisākappaṃ purisavidhaṃ purisacchandaṃ purisassaraṃ purisālaṅkāraṃ.

She isn’t stimulated by this and takes no pleasure in it.

Sā tattha na rajjati, tatra nābhiramati.

So she doesn’t desire to bond with another.

Sā tattha arattā tatra anabhiratā bahiddhā saṃyogaṃ nākaṅkhati.

Nor does she desire the pleasure and happiness that comes from such a bond.

Yañcassā saṃyogapaccayā uppajjati sukhaṃ somanassaṃ tañca nākaṅkhati.

Sentient beings who are not attached to their femininity are not bound to men.

Itthatte, bhikkhave, anabhiratā sattā purisesu visaṃyogaṃ gatā.

This is how a woman transcends her femininity.

Evaṃ kho, bhikkhave, itthī itthattaṃ ativattati.

AN 7.51