The reason I suggested last vote is because it encourages people to work toward a lynch, if it's looking like no one will get lynched. If there's a tie and deadline is coming up, you want to put your vote down on your preferred candidate among the tied players. If it went by first vote instead and your preferred candidate already had the first first vote, you wouldn't have to worry about voting, unless you thought someone else would join the other wagon, in which case you could beat them by just joining the one you like later. But if a lot of people are frantically trying to get the first last vote on their preferred candidate, it will end up pushing both of them toward a lynch. I don't know if that made sense.
I can see how there might be concerns that that one is game-able. But I think if it's close enough to deadline and it looks like no one is reaching lynch number, usually it will be chaotic enough anyway that you can't really intentionally take advantage of it. I think it's actually less game-able than going by first vote. If you go by first vote, early votes carry a lot more weight, and you could probably shift the momentum of the game one way or another by your timing of casting the first vote on someone. That's what it seems like to me, but I'm having trouble expressing that thought. I'm worried somehow it would be optimal in some cases to wait as long as possible before voting someone.
Anyway, it's probably not a big deal anyway, it's just a tiebreaker. I like both ways better than random though.