Got it!

control_FactionName doesn't work. Neither does control FactionName, or anything else for that matter.
Unless...

You play the hotseat game! Then control FactionName works like a charm. The downside is it is only available in Kingdoms. But you can use the Retrofit Mod (only if you have Kingdoms, and you get some other things too). This command toggles between human/AI control, and you could theoretically select only the Mongols as a human faction and wait for them to appear - but that would be quite a wait.

And it doesn't work on games you already started, since it's not a hotseat game.