No, don't usually run overnight. You don't really need to get direction right, just the way they are moving relative to each other. At the moment, for example, I don't really care if the market continues down or reverses back up. All I want now is for FTSE to fall less heavily than DOW if it continues down, or rise more strongly than DOW if it goes up.
I treat direction as a sort of bonus. ie: after I think the relative strength/weakness has reached an extreme (and judging that is the difficult bit) I look to trade FTSE first - if that moves off in the right direction then I hold it as a straight trade and that's a bonus, if it goes underwater I hedge and it becomes a "bread and butter" trade.
jon
ps: yeah just use rough and ready 2:1