Hi and welcome back 
The Rivet is a plug in to the pressure fed oilway that goes through the head to the rocker gear. I gotta say, I don't like these, I had to remove one just last week, but fortunately, the head was on the bench.
Other here may have better solutions, however I drilled the rivet out in the normal way. I checking the oilway though, this did leave a bit of swarf behind and the worse part was the ball end of the original steel stem, was still in there. I was able to bang and poke around to get it out. My preferred plug here is to tap the hole 5/16" UNC (the original drilling is the right tapping size for this), then fit a 5/16" UNC Cup Point Grub Screw with a sealant on the Thread (I use Loctite 243 for this).
Clearly, this is all head off / on the bench work. You may be able to do this all 'on car' and to clean the oilway after removing the rivet and tapping, you would then crank the engine over (not start it), before your chosen plug is fitted and flush the oilway out with engine oil.
Just an FYI, the earlier heads had a Brass Plug fitted here, they were just an interference fit. You could also go this route (or indeed re-fit a Rivet), I'd suggest putting a sealant on the Plug before fitting.