Same thing happened with my 2000. Oil pressure is a big deal to me, so first I changed out the sender, which I guess is usually the problem. Still did it. Next took it to a great Jeep shop and they put a manual pressure reading unit on it. Pressures were all perfect on the manual unit even driving it around for a long time and sitting at idle. He put on a second sending unit, an OEM this time. Did not fix the problem. We then figured it could be the gauge. If you have to fix the gauge, you have to take the entire cluster out and it all has to be documented due to the mileage reading and replace with an entire new cluster with the mileage documented and put on the new cluster. Can only be done by a dealer, takes a couple weeks and costs $1100. So my guy put in a cluster he had in the shop that he knew the gauge worked on to just try it and see if the gauge was the problem. Gauge worked perfectly on that cluster, so we knew it wasn't my cluster. He did a bunch of research and found that this is a very common problem on all Jeep vehicles, not just Wranglers and it is a glitch in the ECM or computer module. So, I had 3 choices since replacing the ECM was out of the question. 1. do nothing 2. put an aftermarket oil pressure gauge on it and disconnect the one on it. However, this also disconnects the battery and water temp gauge alert as all 3 of those are connected to the check gauges light. So, you'll lose that, plus you have to find somewhere for the after market gauge and run that from a split on the sender or 3. Try a slightly heavier oil, like a 50 weight.
Since it is the middle of winter here in single digits temps, for now, I chose to do nothing. On my spring oil change, I will try the 50 weight and see if that makes any difference to how the ECM reads it. If that doesn't work, I'll probably just live with it. One of the things he told me which relieved my mind on not doing anything, was that the later models (he thought 97 on) have a safety switch that if your ACTUAL oil pressure goes below a certain low pressure (I don't remember what he told me, but like 9 or 10), it shuts the engine down/off so that you can't blow the engine. That made it a little easier for me to ignore the flashing light at idle.
Hope this all helps!