Sounds like the oil pressure switch, but is the wire with the female connector actually attached to the alternator, or does it disappear into a bundle of other wires? I suspect the latter.

The O/P switch is screwed into the block at the location you describe. It works by allowing a path to ground (the engine block) when oil pressure is below a set level, I think around 7 psi. Above that pressure, the switch opens and there is no path to ground, so the dash light goes out. Thus with the ignition switch in the on (running) position, but engine off, the wire to the O/P switch should be at 12v and the dash light should be lit.

Does your oil pressure light on the dash come on with all the others when you switch the ignition on?

It's possible that a previous owner disconnected the wire at the switch connector because the switch went bad, and loaded up the connector with grease instead of taping it up.

The low O/P warning is pretty important, so I would get that system squared away quickly.
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