suck
flick, jab, jerk
‘What'll we do with them?’ he asked, jerking his thumb at the suitcases.

raise, stick out
He smiled and raised a thumb in greeting.
I stuck out a thumb and a car stopped immediately.

twiddle (often figurative)
I sat there twiddling my thumbs until the manager finally appeared.

nail (usually thumbnail)

between finger and thumb, between thumb and forefinger
I picked up the beetle carefully between finger and thumb.

thumbs up
He made a thumbs-up sign through the window to tell us everything was fine.

Thumb is used with these nouns as the object:
lift, ride