Oh, I already did that, but there's no way the repair is going to last.

There are two tiny metal clips that sit inside the plastic body of the switch button that ride over the connectors. One of the clips had gotten slightly bent and was preventing the switch from returning to its normal position. I tried to bend it back, but the metal is so delicate and the parts so small that, despite the fact that it works right now, the clip is quite mangled. I'm amazed that it works at all.