Oil will seep into the governor. There is a drain hole which should be on bottom. I discovered this when mine quit working and I found it full of oil. I had the drain on top. This may or may not be your problem. When you pull the cover the contacts are the first thing you see. Clean them.
You can test the governor with your multimeter by chucking it in a hand drill motor. Also, you can check the operation of the solenoid circuit by disconnecting the governor wire and grounding it to the frame.
