Answer: clamup

AnswerCrossword Clue
CLAMUP

"... but they always quiet themselves when I tell them to ..."

CLAMUP

Refuse to talk

CLAMUP

Suddenly be quiet

CLAMUP
Not rat
CLAMUP
Cease talking
CLAMUPShut one's trap
CLAMUPKeep mum
CLAMUPGive nothing away
CLAMUPSay nothing
CLAMUPButton one's lip
CLAMUPStop talking
CLAMUPPlay dumb
CLAMUPQuit talking
CLAMUPWithhold information
CLAMUPZip one's lip
CLAMUPRefuse to speak
CLAMUP"Don't say a word!"
CLAMUPGet quiet
CLAMUPStop responding
CLAMUPHush one's mouth