You didn’t miss anything, it’s a terrible comic. It’s just saying the castaway wants to stay and the woman says yup 3 times in a row. The beacon is unexplained and makes no difference. There’s no point, no punch line, no depth, no dimension. It’s a small sentence about leaving material trappings that didn’t even need 3 panels, an island or a companion.
He says a thing, she’s say yup 3 times, they’re on an island…