They found the Most Mysterious Song On the Internet.
It's actually called "Subways of your Mind" by a German band called FEX. They're apparently going to reunite to do a remade remastered version of it to celebrate it's (re)discovery, and a newer, different recording of it from the same 1980s era is already available.
Here's the version of the song from their Demo tapes - https://www.youtube.com/watch?v=NbKTOuLCg-o
@DrakkenZero I for one am extremely happy about this entire development and look forward to the remaster.