9 pin connector - dash cluster - 69 'Cuda

If you have the panel out, a ohms meter on the 2 oil gauge posts should show approx 20 ohms. Open or no path from either pin to the gauge can.
The connector at the oil sender is supposed to have a plastic insulator on it. It is often broken and MIA. If that bare terminal gets knocked off the sender and touches ground, the zero resistance path overheats the gauge until it fails. If the resistor wire is fried it usually shorts to the beam. Contact posts will be shorted to the gauge can. You might see small particles of cooked insulation like black pepper falling out of the gauge.
There is a aftermarket source for that connector with plastic insulator. I didn't save the link to it but it is in other threads here.
For the oil gauge sender, with the engine running, not know what oil pressure you have, resistance from senders terminal to battery neg' should be somewhere between 70 ohms and 15 ohms.