" oil pressure is in the middle of the gauge" Um, sounds like an idiot guage. The good ole ford gauge wired to a pressure switch, it will either display in the middle or not at all. A real pressure gauge would move all over the place depending on driving, idle and temperature.
To me it doesn't sound like any sort of valve tap I ever heard. The fact that the sound changed when you held the plastic cover suggests that whatever is under that cover, on that pulley, is somehow related or something else moving causing an impulse in that cover.
I don't know the 2.3L. If the engine has a timing belt as suggested, if the mileage or years says it is time to change, or is unknown...having gotten burnt by a timing belt overdue to change failing in a non Ford product...I would be inclined to change it. That only applies if it is an interference engine where messed up timing could result in piston damaging valves.