Google brought me to a post on Cruisers' Forum in which the author said the first thing to know when replacing gauges is that there are three wires: one from the sender, and a positive and negative. Wait a minute. A positive and negative? So those analog gauges need power? So I immediately jumped up and ran over to the boat, fired up Perky, and started flipping switches on the panel, and wouldn't you know the panel has a switch labelled "Instruments" which totally does the trick?
So hopefully someday someone as puzzled as I will stumble on this and it will make their day.