1. You need to have an independent oil pressure gauge hooked up to the engine to check the oil pressures at various RPMs and to verify the 40 to zero drop. This will eliminate any issue with the pressure gauge or the sending unit.

2. The oil pressure variation can be caused by an intermittent blockage in the oil pick up or an intermittent sticking oil pressure relief valve. I would possibly suspect the latter if you are getting good pressure and it is intermittently dropping to zero and going back up again..
If you or previous owners have not maintained the engine with frequent oil changes you will get a sludge build up problem in the engine and this will be evident by just dropping the engine sump.

3. If you have had a check engine light warning then you need to have the vehicle scanned to see what fault codes have been generated by the computer. There will be some related to the intermittent loss of oil pressure but there may be others also..

4. You need to have the oil pressure problem checked out immediately. Running the engine when you constantly lose oil pressure intermittently will definitely cause engine damage due to a loss of both lubrication and oil cooling to critical components.