There is no simple answer to this. The idea is obvious enough that movements existed in almost every country. But for practical purposes, national movements gravitated on what aspect was lacking most in their territory and best aligned with the political views otherwise.
The feminists inside the socialist movement can be said to have properly argued for this universality per se, but ultimately the universality (at least in much of Europe) came more out of a compromise between the left side of the political spectrum (social democrats, socialists and sometimes liberals) who argued foremost for increasing the electorate by eliminating the economic barriers to voting and the (amusing perhaps) counterbalance of women suffrage that the conservatives and Catholics started to support at one point. It was thought (in these latter circles) that women would generally be more conservative and Christian in their votes. (Notably the Pope endorsed the cause in 1919.)
So, in practice, universality came out more of this kind of "horse trading" rather than as a result of some trailblazers who were arguing for it per se having had much impact/following.
(Reference: Ruth Rubio-Marin,
"The Achievement of Female Suffrage in Europe: On Women's Citizenship".)
In Europe, the revolutionaries of 1848 commonly demanded universal male suffrage. A few of them extended this demand to women, most notably Jeanne Deroin (and her followers) in
France and (much more muted) Guiseppe Ricciardi in Italy.
Universal white male suffrage had more or less been achived in most of the US by this time, so the demands for equeality there were (instead) on racial and gender lines. As Wikipedia is much better at covering Anglophone topics, you could look at the American Equal Rights Association, how it was formed as a merger of anti-slavery and suffragist movements... and how it splintered.
It's unclear if the (also 1848) US Declaration of Sentiments
was in any way inspired by demands/events in Europe (or vice-versa), but it's certain that Elizabeth Cady Stanton was also a member of the American Anti-Slavery Society, and the AASS membership was definitely keenly aware of events in Europe; e.g.
Theodore Parker gave a speech to the AASS in April 1848 praising universal male suffrage when it was adopted in France that year
and concomitantly emphasized the French freeing slaves from their colonies. And likewise Lucretia Mott's speech to the AASS
in May 1848 noted how demands for various freedoms had converged in 1848 in Europe. Alas there's no written record of
Stanton's reasoning for why she publicly argued for women's suffrage precisely at Seneca Falls in 1848, but it's been suggested this [1848 year] was not a coincidence; there is some prior private correspondece of hers from 1840 in which she mused about forming a third party to champion women's rights. (reference: T.M. Roberts, Distant
Revolutions: 1848 and the challenge to American Exceptionalism pp. 83-85 and 91-92).
During the revolution of 1789 in France, there were similar attempts at putting women on par with men, e.g. the Women's Petition to the National Assembly. These don't ask for voting rights explicitly, although they can be considered implied, e.g the Declaration of the Rights of Woman and of the Female Citizen substituted "all citizens" with "all citizens including women" in article VI, which spoke of access "to all public dignities".
