The theories about a shared connection were on the correct path.
I finally had time to get into the boat's wiring over the weekend. After tracing the bundles from the console, I located the main ground bus bar. It had a fair amount of corrosion built up on several terminals.
Disconnected the power, then cleaned all the contact points and re-secured the connections. Once I turned the battery switch back on, the horn, speedometer and fuel gauge all functioned properly. The problem is now resolved.