From a 1986 Zappa interview on KPFA:
"I'm going to be doing a video for it (Thingfish), which'll have all the things we've come to expect in a music video...

a girl's legs as she gets out of a car
venetian blinds
an atomic explosion
a girl twirling around in a lap dissolve
a person pretending to be Chinese
and a pair of red shoes

...and I've asked John Carpenter to direct it. Should be out around Christmas."