is using your pointer and thumb simultaneously a better way to do pinch harmonics than just the thumb? b/c you can only downstroke when you have just the thumb sticking out but with the other option you can down/up on your pinch harmonics and keep tempo more easily.
Any way is fine if you can hit them easily and consistently.
I can only do pinch harmonics on the upstroke with my finger. Doesn't matter as long as it works.
Try bending your index finger a bit so you can hit the string with it on an upstroke.
I find that my pinch harmonics sound "chunkier" if I use my thumb, but really, whatever works for you. I can defnitely see it being useful to be able to almost alternate pick those harmonics.