Deere 2840 has a reoccuring noise

I am trying to determine what the noise is in the engine of a John Deere 2840. The engine starts readily and idles fine. Rev the engine up and it doesn't miss a beat. Engine sounds strong. Tractor looks to have been well kept and although the tach doesn't work it only shows 1600 hours. The tractor is owned and used by a Christian camp so I am just helping them out free of charge.

With the hood off, your ear towards the valve cover, and the engine running at a high rpm a slight tapping noise occurs roughly every 3, 4, or 5 seconds. The noise lasts only 1/2 second maybe and really seems to have no relationship to rotating or linear part movement. The noise sounds like tapping a pencil on the edge of a table as hard and quickly as you can. During that 1/2 second there might be roughly 3 taps, then it is gone for 3 - 5 seconds before you hear it again. It continues to repeat. At low rpm's the noise isn't there so much. It certainly isn't a rod, main, or piston.

I thought it might be the hydraulic system calling for hydraulic pressure due to an internal leak and momentarily loading the engine every 3 to 5 seconds. I did remove the piston pump coupler between the pump and engine and the sound still occurs.

I don't know where to look now. I need your ideas. Could it be valve train clearance? Pulsating diesel fuel flow? Air in the fuel system? Thanks for your ideas.

Does pushing the clutch down change anything?

Pull the valve cover off and check all the rocker arms and push rods. I have had worn rocker arms make funny noises.

I to check wear on rocker arms & valve clearance. If noise persists then check injectors for correct pop off pressure & spray pattern.

With the engine OFF grab a fan blade and see if the water pump bearings wiggle. Should not have any. Deere pumps can have that bearing bad and still not leak. Once had a 2240 you would swear the engine was knocking like heck. You could really hear it loud as you set in the seat. Turned out it was a bad water pump. Glad I checked it first.

Exhaust valve rotator? Broken spring? Also check for wear on the rockers where they contact the stem.