C510 Captain reported engine oil pressure indication issues resulted in and engine in flight shut down and a diversion to make a precautionary landing.

Narrative

On Date; I was flying a Citation 510; Aircraft X. I was cruising at 37;000 ft. when I got a Master Warning and a Red CAS Message that said Right Engine Low Oil Pressure; I immediately looked at the oil pressure gauges; the right engine indicated normal oil pressure and was parallel with the left engine oil pressure which also indicated normal. In the time it took me to look at the oil pressure gauge the Master Warning and the Red CAS Message went away; approximately 1-2 seconds. I then verified that all engine gauges for both engines were in the normal range and parallel to each other. Approximately 1 minute later the right engine oil pressure gauge Xed out; I again verified that both engine oil temperatures were normal and parallel. Approximately 30 seconds later I again got the Master Warning with a Red CAS Message that said Right Engine Low Oil Pressure; with no way to check the oil pressure with the failure of the right engine oil pressure gauge I made the decision to do a precautionary engine shutdown on the right engine. I did the memory items for an engine shutdown then my Copilot and I did the abnormal inflight engine shutdown procedure. In the abnormal inflight engine shutdown procedure; it states to 'land as soon as practical'. I notified ATC that I had done a 'precautionary engine shutdown' and I requested a lower altitude. ATC gave me a lower altitude and asked my intentions; I told them that I would like to head back to ZZZ1; I was close to ZZZ2 and considered landing there; but I realized that at 37;000 ft. that it would take me at least 20 minutes to get down to ZZZ2. I started down in a slow decent of 300 ft. per minute; at 300 ft. per minute so that I could maintain my speed while losing the least amount of altitude. ATC asked my intentions; I told them that I would like to head to ZZZ. Company at ZZZ does almost all of our company's aircraft maintenance. I was 42 minutes from ZZZ and at least 22 minutes from ZZZ2 because of my altitude. I did some math and determined that at a 300 ft. per minute decent that I would cross ZZZ at 24;400 ft. I pulled up the nearest airport page on the MFD on the G1000 and always had an airport that I could land at the entire flight.Enroute I reviewed the precautionary engine shutdown procedures; the single engine landing and single engine go around procedures. The weather was good VFR; as I neared ZZZ I had set up the vertical nav on the G1000 for a steeper decent so that I would be at flight idle most of the way to touchdown. Upon landing I was surprised to see the fire trucks waiting for me. Root cause of the issue: Oil Pressure Transducer.