Step 2: Plug the Holes
I used some polyurethane epoxy to patch the holes because it has a bit of flexibility even after it is fully cured. I had some nice Double-Bubble pouches lying around. Regular epoxy would probably work just fine too as long as you don't coat too big of an area as the epoxy might pop off. If I were really clever, I'd find a way to fix this Thermarest in the backcountry.
I opened the valve to deflate the Thermarest before applying the epoxy so that the air wouldn't blow a path through the curing epoxy.
Mix it up on a piece of cardboard pulled from the recycling bin and dab it over the place you marked with the sharpie.
Let it set for a few hours and then test out how well it holds air!