The additional small fuse box is kind of throwing me here--I'm guessing it's not a stock '65 radio?
This is a shot in the dark here, but it sounds like you've got a broken or bare wire somewhere. While the car is sitting still, nothing is moving, and therefore the fuse doesn't blow. When the car is being driven, the wiring is flexing, and this bare wire is probably touching metal somewhere, thus making the fuse blow.
Bottom line--if it only does it while driving, then something somewhere is moving and tripping the fuse. |