Cluster Woes

No way for the oil pressure sending unit to "burn out". It's on the back end of the circuit, not the supply end. Power goes through the instrument cluster, warning lamp, and then back out to the sender on the engine. The sending unit is just a simple on/off grounding switch in a car with a warning light. Oil pressure keeps the switch open and the light off. Low or no oil pressure allows the switch to close and complete the circuit which turns the light on. I suspect you have some wires crossed somewhere if the sending unit is getting straight 12V without a load (like the light) further up the line somewhere.