We had the very same symptoms with our 66 289 oil pressure gauge when be bought the car last September. By looks, the engine had been rebuilt some years in the past but the PO neglected the car and only put on less than 1000 miles in 9 years. The car also had a terible lifter noise clatter on the right side.
When I brought the car home I changed the oil and put in a treatment. The noise diminished noticibly after a few hunfred miles.
I also noticed that the oil presure switch lead wire was worn and changed the switch and lead over the winter.
Because the car is not yet ready for the road I have not yet been able to check out how the gauge works now. Instrument cluster still out.
I figure the engine is possibly sludged and has issues from standing idle for so long, as I get a lot of "blue" smoke and "black" gunk out of the exhuast pipe when I start the car. Could I have both "oil" and "fuel" issues? Probably!
Once I get the car rolling, hopefully this weekend, I can let you know if the new sender/lead helped.
If not I am going to pick up an oil presure gauge and test each cylinder individually. I really think the engine needs an overhaul though.
I might look for another 66 289 to rebuild next winter. I have never done it and sounds like fun. I can then add some performance modifications. Then put this engine in the car while the original is rebuilt to stock.