My radio and wipers sometimes come on with car off and keys in my pocket....wondering if anyone can help.

1984 190d, 2.2L w/5 spd manual. Has 427xxx miles and still gets almost 40mpg running 80% WVO blend. Paid $500 for it 4 years ago and probably the best car I've ever had.

Here's the problem:
-about a year ago, the radio would turn off with the ignition switch, but would occasionally turn itself back on as I was exiting vehicle with keys in my pocket. Quick inspection found mild corrosion in fuse panel near this fuse. Cleaned off corrosion and this seemed to resolve problem.
-this radio problem recurred and became more and more frequent so I started just removing faceplate everytime I exited car and this seemed to resolve problem.
-about 3 months ago, my wipers would do the same thing...turn off when I turned off car and removed key, but turn themselves back on. I never witnessed the moment they came back on. Rather, I'd look out from work or into my garage and see them sweeping happily back and forth.
-To address the wiper problem, I simply replaced the wiper/turn signal switch with a brand new switch assembly. I'd already been planning on doing this since the turn signal canceling cam in the old switch had gone bad.
-This made a temporary improvement, but like my radio, the problem recurred and got worse. I ended up removing the wiper fuse entirely. Now I can't drive on days it might rain. Nice.

Now, everytime I go out to drive somewhere, my battery is dead. Battery is ~6 months old, brand name and plenty large for application (~800CCAs). It will charge up fine with trickle charger and load tester tells me it's good, but something in my car keeps draining it down!!!

I need to figure out the root cause of my problems. Could a faulty ignition switch cause this? How would I test it? Could wipers/radio possibly be unrelated problems? What could be other causes of my problems?

I appreciate any help!

Best,
Brad