Down To Two "issues' Can Sure Use Some Help

Top problem: I take it that you are not the first owner of this car...
Electrical gremlins from two totally unrelated electrical systems means that you have one of 3 things:
1.) Low voltage due to a power delivery problem to the top.
2.) A bad ground in the top motor circuit - not so likely since it would also show up when raising the top.
3.) A miswire due to the efforts of the previous owner. That's why I asked if you were the original owner.






Vibration problem:
Check the accessory drive belt and pulleys. Start the engine and have someone hold the throttle at the point where it vibrates. Closely examine the belt and pulleys; if you see the belt vibrating, the belt is too long or the tensioner isn't working properly. The tensioner has a mark or pointer on the front which should not point to the extreme end of travel on either side.
Or...
You have an accessory with a bad bearing or internal damage. The smog pump is the first suspect in this scenario since the vanes inside the pump often fail. An automotive stethoscope is an inexpensive tool that can be very useful in diagnosing mysterious noises and vibrations.

Watch the harmonic balancer to be sure that it isn't wobbling. If it is, replace it.