machine part, 1745, apparently from tap (v.1) + -et, "but the use of the suffix is abnormal" [OED].
Entries linking to tappet
tap v.1
"strike lightly," c. 1200, from Old French taper "tap, rap, strike" (12c.), from a Gallo-Roman or Germanic source ultimately imitative of the sound of rapping. Meaning "to designate for some duty or for membership" is recorded from 1952, from notion of a tap on the shoulder. Related: Tapped; tapping.