<<Switch #5 does not seem to work as I have background music with the switch on or off. Perhaps the physical switch is bad? I’ll test that tomorrow.>>
If the switch was actually stuck on it still wouldn't cause background to be stuck on at game over, switch is likely okay anyway. Wasn't a real good test for me to suggest for your problem.
<<Grounding each sound line produces a sound. Grounding pin 2, sound 16 produces no sound at all.>>
Sound 16 line sounds like it is stuck 'on', whether on the sound board itself or at driver board. You could try disconnecting sound 16 wire from the sound board connector and see if background problem then stops, to help isolate where it's stuck on.
Your other tests via the test button and the dip switches sound okay.
However - - - Sound Mapping is: "20 - 10100 - Background music or Lower PF wind". Sound 16 on by itself (10000) isn't assigned a sound. So maybe your sound line 4 is stuck instead? But by your tests, sounds like 4 is okay.