[villagetinker]

I would also check the ground connection, especially if both lights are going out at the same time. The other common components to check, the headlight switch and the connections for this switch. The main fuse and the key switch also are common to the engine, so you would see the engine stutter or shutdown. I have seen problem with wiring harnesses and the older style Halogen lights, but not the newer LED lights.
If you are a DIYer, you can turn on the headlights and jiggle the wires while observing the headlights, you can also remove the dash panel and do the same with the wiring in there. If you find the loose wiring, then you should be able to apply a fix.