Hi there, not sure if you've done the oil pressure switch yet, but if not, PLEASE LEARN FROM MY HORRIBLE MISTAKE:
I have a K4 as well, and had the same issue as you. The oil pressure light would pop on at idle once hot, but my pressure gauge was showing more than adequate numbers (I did Elan's pump rebuild, etc). My old pressure switch threaded into the case until it was flush. I ordered a replacement online and it had a different TAPER, as a result as I threaded it in, it acted like a wedge and it cracked my engine case. Oil poured through the crack in the main oil galley. I ended up having to source a new engine as two attempts at welding it failed.
There is a torque spec for that switch, and a specific thread pitch and taper required. I have no clue what it is off hand, but be sure to check.