Q: Fog lights staying on after jumpstart.

The fog lights are turned on and off at the switch and the body control module controls when they come on or go off. This is not common but you may have a short in the system that is keeping the lights on from the jump starting. The body control module may have shorted or the fog light relay or fog light switch is shorted. You could remove the fog light fuse in the engine compartment till you get it looked at by a certified mechanic that could trace and see if the switch, relay or body module is the cause of the short. Jump starting can spike your computers in your car or the other car. I always recommend to jump a vehicle by not running the good vehicle and only using that vehicles battery and not their charging system.