The first thing to do is determine what is causing the discrepancy between the oil pressure alarm/ light and the oil pressure gauge. My recollection on the TAMD 40 engines is that the gage pressure sender and the oil alarm switch were both mounted on a single "T" fitting which was screwed into the oil gallery on the STB side of the engine block, just adjacent to the oil cooler housing, similar to the photo supplied by Catalina Jack. The alarm switch is the smaller of the two....if you disconnect the wires from the alarm switch the light should go out. If you want to install a mechanical gage, there are several 1/8" pipe thread plugs along the gallery on the Stb. side of the engine, same gallery that the senders are screwed into.
As far as the tapping noise......adjust the valves first. Regarding the side to side rocker arm play on the front and back of the rocker arm shaft....it shouldn't be there. All of the rocker arms are able to float from side to side a bit, maybe even an 1/8", but there should be springs on the rocker arm shaft that lightly press on the rocker arms. This spring pressure keeps the rocker arm pressed against the shaft support bracket or the snap ring on the shaft. It shouldn't allow any tapping noise.
Some one mentioned that the tapping might be a broken spring in a pressure relief valve. Your engine has two spring loaded pressure valves that might be causing noise, one on the front end and one on the back end of the oil cooler mounting bracket. One of these is the piston cooler valve. ( opens at high pressure to allow cooling oil to spray on the bottom of the pistons) The other is either an oil filter bypass valve ( for plugged oil filter) or a high pressure relief valve.....I don't remember which off the top of my head. In any event, when these valves act up they usually cause a buzzing sound, not a clicking sound. They are easy to disassemble to check the spring. This should be last on your list as they are fairly trouble free.
There is nothing that you can set or adjust with the injectors on your engine, but it's possible that they be a bit dirty or need servicing, and that could be causing an occasional rough combustion rattle, particularly at low RPM and lower head temperature. Can't hurt to have them serviced, especially after 1350 hours and what....35 years?
DougR