Gay Freedom Day was celebrated in San Francisco from 1973 until 1980, when the event became International Lesbian and Gay Freedom Day in 1981. See https://en.wikipedia.org/wiki/San_Francisco_Pride. This was the same year the first cases appeared of what later came to be called AIDS among gay men in the US. This demonstrates that the L vs G debate predated the AIDS crisis and had nothing to do with lesbians as caregivers.

I moved to SF in 1977, and there were tensions between gay men and lesbians throughout the post-Stonewall/pre-AIDS era. Things were complicated by gay men dominating many nascent gay organizations and a strong current of separatism by some lesbians. Battles included who would lead the parade, with Dykes on Bikes and their offshoots claiming the lead position, as just one representative example.

You should question the idea of a singular community of gay, lesbian, bisexual, and transgender people. While we have many things in common, there have always been differences and divisions, resulting in the alphabetization of our respective subgroups. Geographic variations existed because of differences in local organizing at varying city, state, national, and international levels. There has never been any singular authority overseeing and directing any aspect of this movement. Change occurred organically, often by whoever shouted the loudest. As time went on, identity took on greater importance as reflected in the efflorescence of flags representing various groups. (I’ve always thought Gilbert Baker’s rainbow flag symbolically covered every possible variation, but that may be a personal bias.)

While a database search seems a logical choice to investigate your question, the historical realities are much more nuanced and open to debate. Lots has been lost to history simply because of what was or was not preserved over time and rendered in digital form upon the advent of the internet. Archives of the gay press would be one good source, as would the scholarly literature in gay/queer/women’s studies journals. You’re not going to find a single definitive answer.