This is probably a stupid question, but does Pawn of the Dark Side require you to follow legal targetting rules to pick the character who gets the extra turn?

Pawn works basically the same way as Dominate. With Pawn (and sometimes Dominate) you are targetting an Allied character. Anytime you are targetting an allied character, you cannot follow the 'rules for targetting' at all, because those only apply to enemies. Any time you use an ability on an Ally, it can be used on any Ally in LOS, as long as they meet the Range restriction as well.

So, even if an enemy is adjacent to Sidious, you can use Pawn on a piece that is across the board somewhere, as long as you have LOS. Same holds true for Dominate if you are 'targetting' an Ally with the ability.