Oil pressure problem

You oil pressure sending unit has gone bad, it's common to go bad and some even leak oil. 
The oil pressure sensor is on the back of the block on the passenger side, you can get to it from the top and not from the bottom. There are (2) switches back there that screw in to the block and you can only see it from the top of the engine. The Oil Pressure Sending Unit is the one wire harness with a green and white strip on it. The other switch has more wires to it. 
When you pick up the new sensor, make sure you get the right one. make sure you get the Oil Pressure Sending Unit which sends variable oil pressure and has only one quick connect for the wire connector. The oil pressure switch is the one that only activates the oil light on older engine. 
Once you get the right part at Auto Zone for around $9.00, disconnect the wire clip with the green with white strip on it. and use a deep spark plug socket with a extension and u joint to get the sensor out. The sensor comes with teflon tape already and no oil should leak out from the block. It as simple as replacing a bolt and reconnecting the wire connector. 
Good luck and hope this helps, take no more then 10 min to do but about 5 hours for the engine to cool off LOL

Check big end and main bearings for wear,Also check oil pump is not worn

Sounds like you have a short in the oil pressure sending unit or the plug may be loose. I would check online for the location of the unit, not the oil pump but the oil pressure sending unit, should be electrical, and when you changed the thermostat you may have got the plug-in loose somehow. I hope this is helpful in some way.