My Void Elf would probably end up being the founder of a small group of Void Elves that decided to isolate themselves from the Alliance so that they could pursue their research in a safe, remote location away from civilisation. Away from anyone that could judge them or attempt to stop their efforts in any way. And this is what they’d do at first. Not outright hostile, but disinterested in maintaining good relations with either of the factions that have “abandoned” them and sticking to themselves, living off funds that my character has been saving up over the years.
Of course, Void is considered dangerous and not very trustworthy for a good reason. The longer this sort of research continued, the more their minds would degrade and the more difficult it would become to resist the Void’s influence. It wouldn’t be a Void cult in the traditional meaning of the word (my character realises that the Old Gods are not on their side), but they wouldn’t be beneath recruiting more Thalassians to their cause or assaulting Alliance/Horde settlements for supplies once they get close to running low on those.
Eventually, the group would become large and dangerous enough to gather the attention of both Alliance and the Horde, resulting in them being chased down by the factions and forced to remain on the run. The faction would probably not prove to be a very lasting one and eventually, they would be all either imprisoned or wiped out… the latter not without taking those who went after their group with them, of course.