Engine tapping sound?

That is not a sound you want to hear in an engine. As you can notice when you disconnected the coils the sound changed from the loud click to a dull thud when you pulled the coil connection on cylinder 4 (middle cylinder). That indicates it is a bearing problem in the engine. Valve train issues wouldn't change in sound that way. If the rest of the car is in very good shape you might consider either a used engine or a rebuilt one.

No this sound is usually from bad bearings on the connecting rods inside the engine. It's also possible that this is a damaged piston but that is rare. This will require the engine being torn down and checking the internal parts to repair it.