From what I've read, it will run even with low oil pressure, but some damage can be done to internal bearings, so it's better to verify with a gauge.I agree, probably the switch. My OP gauge quit working and I got a low pressure warning a few years ago. The switch just needed replaced. I don't know if the truck would even run if your low oil pressure was below the threshold where the warning message was supposed to come on. But I know very little, my truck idles at 4500 according to the tach.
Mine is so fast, sometimes it runs 20MPH sitting still at idle, so it sounds like you and I both need to send our instrument clusters in for repair LOL