This sounds kind of like what I'm doing with the language I'm making at the moment! But I have different auxiliary verbs according to gender, number, and person and then different endings for the verbs to indicate tense.

For example:
O coma. – I eat.
E coma. – He/she eats.
Eno* coma. – They eat.
Emo* coma. – We eat.
Eto* coma. – You eat. (singular)
Eso* coma. – You eat. (plural)

* These can end in o or a, which indicates gender: o is masculine; a is feminine.

Tenses:
Eto coma. – You eat. (present)
Eto come. – You ate. (past)
Eto comi. – You will eat (future)
Eto como. – You, eat. (command/imperative)

I haven't figured out other tenses and stuff, but this is basically how it works in the language I'm doing! Also, I realize that e/eno/eto/etc. kind of works as a pronoun, but it's required every time a verb is used, even if the sentence already has a noun, so it's kind of like an auxiliary verb.

No, they're still pronouns, not auxiliaries. This is a feature of, for instance, most spoken varieties of Northern Italy. For instance, Venetian:

Me pàre l'è là che'l parla. "My father is speaking." (Lit. "My father he's there that he speaks".)

Not how the masculine singular subject pronoun l (shortened from ed) is present in both clauses even though the first begins with a noun phrase.

This is also a feature of colloquial French, e.g. Louis XIV's famous dictum L'état, c'est moi! This is conventionally translated as "I am the state", but literally it's "The state, it's me!"

My bad. I guess it makes sense now that I think about it that way. I just always thought of them as auxiliaries because they evolved from the Cakuacakuán endings which indicated tense, number, and person. They themselves were inspired by the Spanish endings, although in a slightly modified form.

For example, here is he present-tense conjugation of "kocinal" (to cook).

He is cooking. – Êo kocina. – E cuizina.
She is cooking. – Êa kocina. – E cuizina.
They (male/mix) are cooking. – Eno kocinani. – Eno cuizina.
They (female) are cooking. – Ena kocinani. – Ena cuizina.
I (male) am cooking. – Îo kocinâo. – O cuizina.
I (female) am cooking. – Îa kocinâo. – O cuizina.
We (male/mix) are cooking. – Emo kocinami. – Emo cuizina.
We (female) are cooking. – Ema kocinami. – Ema cuizina.
You (male sing.) are cooking. – Eto kocinati. – Eto cuizina.
You (female sing.) are cooking. – Eta kocinati. – Eta cuizina.
You (male/mix pl.) are cooking. – Eco kocinaci. – Eso cuizina.
You (female pl.) are cooking. – Eca kocinaci. – Esa cuizina.

And here's how the tense was determined, at least in terms of "-el" verbs. I don't know where the chart went that I had. :/

He read. (past tense) – Êo jéĉeua. – E jeche.
He is reading. – Êo jeĉe. – E jecha.
He will read. – Êo jéĉeue. – E jechi.

It's pretty unusual for independent pronouns to evolve from verb endings, but it does happen. The two cases I can think of both involve the first-person plural: Connacht Irish muid (replacing sinn, which is still used in more southerly dialects) and Ladino mos (which descends from Old Spanish nos with the initial consonant changed under the influence of the verb ending).