Thank you both for your replies!
I checked the 6 allen head bolts and the big crankshaft bolt, all are tight and the crank and pulley seem to be rotating smoothly.
Here's an update to the source of the tapping:
After some more digging I found that the upper chain guide and the idler gear of the timing chain both have a lot of lateral play in them. These are 85 and 98a in the picture, respectively. Running the engine with the valve cover off revealed that the idler gear visibly moves back and forth, in the direction to and from the radiator.
My question is, would the play in this idler gear possibly the culprit for the tapping sound? If so, what is the procedure to changing only one of the timing chain gears? Haynes has this, but only for a complete engine teardown.
I probably need to check the chain stretch as well.
Thanks!