If that was hard to understand, let me try again:
I hold my pick the way I normally do, something like this:
When I want to hit the harmonic, I down pick with the second knuckle (the one closest to the fingernail) of my middle finger touching the string. The second I push the pick down, I pull my knuckle off the string, sort of towards me, which (often) results in a pinch harmonic. It's not very easy, but it sounds a lot easier than how Akira described it. Do they sound clearer using the thumb, or what?