What is the verb for the action of a coward?
"Cower" may be the verb you remember. One of its meanings is "to sink through fear".
Cowards are multifaceted!
In addition to cowering, they can flee, retreat, shy away, recoil, flinch, hide, quail, tremble, shrink, wilt, blanch, wet themselves...
The coward displays cowardice. He or she commits an act of cowardice. Cowards behave in a cowardly manner. If especially egregious, the act in question is craven.
There’s ‘funk’ meaning ‘to flinch or shrink through fear’. In the US, apparently, ‘flink’, means ‘to behave in a cowardly manner’. (OED)