With the rocker arm assembly on the bench, you'll find wear and the resulting clatter. Back when it was in service, there was a set amount of rotational rock that the rockers could move with the cam lobe lift, thermal expansion/contraction, and lash set during tune-up. Along comes oil formulas better suited for hydraulic-lifter-type valve set-ups, or, the engine was just from performing hard work. Now, the circular rocker shaft is looking kinda D-shaped, the face of the rocker is like what Mark - 65swb45 was describing, and there is probably also less cam, lifter, pushrod - it all wore away. With that wear, you get a step where the wear begins on the 'D' of the rocker shaft and bushing, and if you keep the rocker within that worn-out zone, no audible click with the rocker arm assembly, at least on the bench. However, when you adjust the length that the screw protrudes on the rocker arm, the rockers might have to rotate past the little worn-in step on the rocker shaft - hence the click.
Regardless, it must be like hammer-striking-force. When the engine is running, it goes from some lash and zero pressure on the valve stem face, to a force that can overcome the pressure of compressing the valve springs, back to a gap. A thin film of oil is the only cusion for wear and friction. I'd bet that they sounded kinda rough back when they were new.