I clench much more now that I have applied shrink tubing to my bits. It really depends on what I'm doing with my hands (typing, for instance, or assassinating a tomato hornworm which was trying to get my pepper plant) whether I hand hold or clench. I do hold my meer in my hand some, but I'm pretty meticulous about having clean hands when smoking the meer.
It's almost always on the right side, but I do center-clench sometimes, which I haven't seen anyone mention yet.