Take a look at your brake lamp modules. They're easy to pull out from the trunk, no tools required. Any melting of the bulb sockets, charred wiring, melted sockets in the bulb holder? Are the dual filament bulbs long life, preferably sylvannia LL? A short in either brake module can cause the conditions you describe.
Having to use the shift lock to get out of park sounds like one of the two brake pedal mounted switches has gone bad. See the BR (brake) section of the FSM or search the topic in the Q45 forum. Others have had the same issue.
The 1994 FSM is the oldest available but I like using the 95 FSM since it has an index. It's 99% the same car as yours and will work fine.
http://www.nicoclub.com/FSM/Q45/1995_Q45/
Welcome to NICO. Come on over to the Q45 forum and introduce yourself and your Q.