I strongly suspect a live wire that moves when driving and grounds itself. It may have it's insulation worn off and touching somewhere. This specific situation can be a pain to find because it shows up only when driving You have to proceed with elimination. You could remove the fuse box from the firewall and see if anything is loose back there. Go under your dash and with the switch on and lights on, move wires around. Look around tail lights and headlights where wires may be touching metal. This may be a detective game if you don,t have an obvious culprit. To give you an example, I once had a Renault that refused to start one morning after running perfectly fine. It did not turn over at all. After eliminating obvious possibilities, such as fuses, battery, starter and the ignition switch itself, I gave up and brought it to my mechanic. He eventually took the whole dash apart and traced every single wire.
He calls me up after a week to ask: 'Do you mind if the rear light does not turn on when you open the door? Because when I cut power to that wire, you car starts.' Unexplainable, but that solved the problem. Give me a mechanical problem over an electrical problem anytime. Best of luck!
