Neutral safety switch...
You didn't say what your car is, (Seems like you used to have a 280) but if it's transmission is situated like the one in both my Mercs was, it's actually mounted on the transmission itself, on the left side where the shifter rod exits the transmission case. The wiring harness comes through a hole in the tunnel very close to the location of the accelerator pedal, and there's a connector right there. You might see if the connector is loose or damp, and you can always bypass the switch connections for the starter circuit as a test, there's only 4 wires in the connector - 2 for the backup lights, and two for the starter circuit.
You could always replace the whole thing with a 4.3L V6 and 700T4 Tranny like I did on my '82! HAH! (I stilll haven't had any problems at all with the conversion)