Horsemen of the Apocalypse

In my two most recent games, I had the Four Horsemen turn up. At the time I was top in score, and seven out of eight spawned right next to me.

Is score a factor in where they (or the other late-game spawns) spawn? And if not, what affects their spawn location?

I'm fairly sure it's totally random. Perhaps your empires covered a large area, which would make it more likely for them to appear somewhere you own.

The only reason why the other one didn't go after me was because it was on a different continent. In the second game I got piled by the last three all at once.

Maybe setting the game to Last Days wasn't such a good idea. Especially in the second game, which got to 75 on the counter without anybody being Veil.

The spawning is random, but Barbarian AI isn't completely random: if I remember correctly, it executes an AI warplan just like any other AI race, which targets one specific civ at a time. Every X turns it switches to a new civ, weighted towards higher scores. To see this in action, put on raging barbs and boost your score in WB. Wait till you have a steady stream of barbs and then go into WB again and have a look at barbarian movements: you'll see they are even moving through other AI's territory, ignoring their cities, to get to you.

The Horsemen use AI warplan just like any other barb, so even if they spawn far away, if you're the current target they'll walk halfway across the world to get you. However, because they have such high movement, they'll often get sidelined with 'targets of opportunity': IIRC AI will prioritise very weakly defended cities and workers above their set AI routine. You can actually abuse this in-game by moving workers away from your cities as bait if you need to buy a turn or two.