should be just as good as connected to the battery . ground strap replacement is a good thing however the pickup is rubber mounted well should be, have the taillights got a good return path to the chassis ? temporarily connect a wire from the taillight mount to a chassis bolt both clean connections see if that improves if so problem is an earth issue at taillight , also test that you have 6v at the pin inside your light fitting could have a corroded connection somewhere
regards
andrew
