First of all I have a 1990 Z32 NA and I'm puzzled about a connector that is attached to the left timing belt cover. I'm asking this because when I bought a new timing belt cover, it did not have the screw holes to mount this bracket with the connectors to the cover. The reason I want to do this is because the previous owner cracked the timing belt cover because he tried to yank it off without taking off the two pipes that block it's removal. So I'm unsure if it's some kind of sensor, which I doubt because it's attached to a piece of plastic. Any ideas?

 

If you mean left as in when you're facing the engine, that's where the PTU would usually mount. If your Z runs, the PTU must've been relocated elsewhere (the PTU is vital for the engine to run at all).

P.S. There's a reason we say "driver's side" and "passenger's side"... it avoids the issue of "left when you're facing the engine."