Trailblazer oil pressure issue

I have a consistent issue with my 2004 Trailblazer where the oil pressure will slowly drop from 50-60 psi all the way down to 0. Like I said, this happens consistently and it takes around 10 minutes or so for the oil pressure to drop down to 0 when it is hot. When it is cold it takes around 15 minutes for it to drop to 0. Those times probably aren’t the most accurate, I don’t exactly time how long it takes for it to drop. What is having me stumped though is the fact that after shutting the car off for even just a second and then turning it back on the pressure will rise right back up to 50 psi but begin to drop again. After turning it back on more throttle will make the pressure go higher, but as it slowly drops throttle begins to make no difference in the pressure. As a matter in fact, it almost seems to make it drop quicker. I know that all of these pressure readings are indeed correct though because I put in a mechanical pressure gauge so I am not relying on the one in the dash (because it is simply just a switch). Does anyone know what this problem is caused by????? I don’t want to immediately blame the oil pump or the o-ring on the pickup tube because if either of those were bad, the car should NOT re-gain all of its oil pressure, let alone within seconds.