I think that if additional information about factions is going to be revealed, the logical time and place would be when a negotiation fails for reasons that would not be immediately obvious from things the Elector has said or is discoverable about them (e.g. an Elector not voting for Zorana because of an assumption that an Investigate Elector would have dispelled wouldn't count). Something a bit like gur rcvybthr jurer gur Hhmtun tybor vf haqrefgbbq, ohg eryngvbaf ner fgvyy cbbe; gurer vf n uvag gurer gung Mbenan znl unir qbar fbzrguvat ryfr gung hcfrg gurz. Vg qbrf abg fcrpvsl jung gur bssrapr jnf, ohg vg tvirf rabhtu pyhr gung n cynlre pna erpbtavfr gung guvf vfa'g whfg punenpgrevfngvba, ohg fbzrguvat gung Mbenan pbhyq punatr ba n qvssrerag eha.
An intuitive feel that certain Electors are affected by certain actions is useful to acquire, but you've done a good job of that already by the way you've characterised the Electors. Bonus: some of that characterisation is available to all Zoranas via the history of a specific run, and a fair bit more to many Zoranas through investigating Electoral backgrounds. I certainly couldn't name all the factions, but once I've met, investigated and negotiated with an Elector, I feel like I have a good idea on what is likely to influence that Elector and how. I feel like the factions are as much to ensure consistency of characterisation (to support what is said about each Elector from sources the player has) as it is about dropping hints to the player.
(Ethexae is the Elector that jumps out at me as someone whose reasons for declining Zorana post-quest are sometimes but not always obvious. That said, obscure motives are part of her character, especially from the viewpoint of someone low in skills/knowledge she thinks are important. So even if you go down this route, it wouldn't be necessary to use the same skill each time, or even for it to be possible with every Elector).