I could be wrong since I haven't changed my bulbs in a while but, I believe the FJ's headlight bulbs are dual filament. So the DRL's and the lows run off one and the high beams run of the second. You might want to double check your bulbs just in case. Hope this helps.
I've had this happen in two different vehicles with aftermarket bulbs where they both burned up within minutes of each other. I think the only thing they share in common is the HEAD relay and that is also shared with the high beams, so it is clearly working. Your bulbs just went out or you've got very picky rats that only eat low beam wiring.