Freaky Electrical Problems Need Serious Help

I would say its your voltage regulator or possibly the alternator itself. Normally I would say its your alternator from the symptoms you gave. The system works like this. Your battery initially supplies the voltage to charge the coil for starting. Once the engine starts the solenoid (also could be here) switches to allow the alternator to now supply the charge to the coil. If the alternator does not take over then the engine gets its juice to charge the coil from the battery itself. If thats the case then your battery is working overtime charging the coil. Now add another drain on the battery such as putting the top up and now you've taken that power to the coil away cause the battery cant handle that kind of demand. Hope that makes since. I dont think you have a short. I would first check to see if your solenoid is wired right then check its operation. replace it cause they are cheap. Next make sure the alternator is wired right and check its operation. Next check the voltage regulator. Hope this helps.