Well, since he's already taken it to two shops to have the valves adjusted or find the noise, I think any advice of not driving it may be a tad late.
And unless the engine has grenaded, I personally want to try to locate the source and cause of the noise as closely as possible before a teardown that officially means the end of listening for any noises with the engine running.
But, if we need to go down this path, just replace the coil.
Nobody believes in logical step-by-step troubleshooting anymore, or following any kind of preliminary guidelines and reporting back so the path can be adjusted to get us all to the source of the problem.
So we just follow the "common wisdom" and replace the coil, mark it fit for duty with iodine, and off we go.
Done.
Yeah, I'm finding this to be true, more often than not anymore. I also follow another BB, that deals with another make that I own (from another country), and have wasted a lot of time trying to convince this guy that his electrical problem is a actually symptom of another problem. He's asked about three times if he can just replace the blown item with another new part-which hasn't worked at least twice. I keep trying to explain why the next new one won't probably work either, and what to look for that is causing the new parts to fail. I've now given up, since he's apparently not getting the answer he wants.
Back to the original question: The noise may or may not be a terminal thing. The suggestion of using a timing light to isolate a top end or bottom end problem is an excellent one. Once that is done, if it is in the valve train, then proceed with trying to isolate which valve or cylinder is the source. Lightly placing a finger on each rocker arm, and finding which one syncs with the click also works (Disclaimer: Don't try this at home, YMMV, etc!). If it's the bottom end, then it might be time to tear it down.
Years ago, I never could get the valve lash to be correct in my TR4, and it rattled and clicked. Drove me nuts. Turned out to be the rocker bushings and the shaft were worn, AND the face of the rockers were dished, as one poster already suggested. Rebuilding the rocker assembly solved the problem. Checking for a bent push rod is also a good idea; but WHY did it bend?
Another time, a friend (we were in high school, so no further explanation is necessary!) shaved the head on his TR4A to raise the compression. It ran like crap, and made all kinds of noises. We later found out from the "old guy" (probably about 40 at the time) that ran the local import shop, that the push rods needed to be shortened by the same amount that was taken off of the cylinder head's face, or the rocker arm geometry would be altered so much that the valve train couldn't work properly. This was actually described in the Performance and Tuning section of the Robert Bentley manual that I had. The car ran fine once he fixed that-wasn't much faster, though.
Good luck. I wouldn't panic yet, but don't run it any more than is necessary for troubleshooting until you have more information. Jim