it's from the episode now titled 'Smile, You're on Mars Camera'

Right on, Lunk! I'm a huge Gilligan's Island aficionado too, and that episode takes the absurd comedy of the show to its most, er, "absurdest." But like the show as a whole, there are all sorts of little, subtle bits of comedy in there in addition to the broader stuff. I like the moment when the two quasi-NASA technicians are monitoring the Mars mission, and one of them gets a buzz on his headset. He pauses a moment, sneaks a surreptitious look down at his nametag, then says, "Bancroft here" (causing his partner to roll his eyes in silent derision).

By the way, the reply to the line I posted is: "I can't be sure, George, but I think he's trying to force him to lay an egg!"