1986 560SL Radio/antenna go on when car is off?
 

I have a 1986 560SL with only 112k miles. Over the last year, the Antenna will go up (or down) completely on it's own when the car is off and the key is out of the ignition. Sometimes the car will have sat there idle for two weeks and I will just watch the antenna go up and down, up and down. Even when the car is on and I turn the radio off, the antenna MAY stay up and I will hear just static through the speakers. Then maybe 10 minutes, 10 days - the antenna will go down and the static stops. It doesn't seem to make a difference whether there is a key in the ignition or not. It is however, draining my battery. Has anyone else had this issue and if so, what is the solution?

And the latest after charging the battery again - now the instrument panel doesn't work. No gas gauge, RPM's, speed, odometer (that's one way to keep the miles off).... but the clock and fuel efficiency gauge are just fine...hmmmm.