For the record (in case it wasn't included above) the oil pressure warning light is for low pressure, not low oil level. An engine can happily put out 60psi pressure until it runs out of oil to suck from the pan. What may happen when the level gets really low is that the light may come on as the oil sloshes around and leaves the pick-up uncovered for a few seconds. If your oil light flickers at idle (car stationary), it may be trying to tell you that the pressure is below -7psi? I think. Which could be that your idle is too low, your oil choice is too thin, your bearing clearances are too big, your oil pump is tired OR yes, perhaps your sender/wiring is flakey. If memory serves, the light goes on if the wire to the sender is grounded (ignition on). In which case, having the light always on could be an electrical issue. But it could also be that you have no oil pressure.
I'd be checking actual oil pressure with a gauge (try Harbor Freight), and then main and rod bearings in situ with Plasti-gauge before getting carried away.