Resolves based on whoever is actually on ballots at the time votes are cast. Vice presidents don't matter, someone becoming president after an election for any reason doesn't count. In 2024 this would have resolved "Democrats". I will resolve based on candidates' stated gender identities when the election occurs.
The tie case occurs if both parties run female candidates in the same election.
Note that the fourth option only comes into effect if a female president WINS the election having run as third party or independent. This option is to account for a third major party without requiring a subjective determination of what "major" means. If a third party female presidential candidate wins but Democrats or Republicans also ran a female candidate, this resolves "It's a tie."
I may trade in this market.