P180 Avanti pilot reported engine oil pressure fluctuations during cruise. Pilot performed inflight shutdown; diverted; and landed safely.

Narrative

At around XA40 I had leveled off in cruise and were monitoring systems when the left oil pressure gauge began to pulse between the yellow arc and the green arc. Out of concern I requested to head into ZZZ where the main maintenance facility is for the aircraft. It continued to waver as I descended so I advised ZZZ center of the indications and asked for minimal delay into the terminal area. We approached ZZZ and the wavering continued and progressively worsened; though no other parameters differed from normal. I brought the engine to idle at this time and feathered it hoping to stabilize the oil pressure indication. It continued to waver in the yellow arc as we descended just south of ZZZ1 [airport] until it eventually would touch the red lower limit in its movement. At that time the engine was shutdown and secured for landing. ZZZ Approach was advised of the precautionary shutdown and that we would thus [request priority handling] and continue with the planned approach into ZZZ [airport]. I advised tower that we shouldn't need assistance and should be able to clear the runway. I landed without incident and after a longer rollout cleared the runway and taxied to the maintenance facility hangar after confirming ARFF (Airport Rescue and Firefighting) did not see any issue or fluids leaking from the aircraft.Believe all training and best practices out of an abundance of safety and precaution we're taken correctly in advising of the problem early and starting in the right direction of where the problem could be addressed.