You could try something like this: https://www.amazon.com/Infinite-Timing-Switch-Module-Display/dp/B074TG32GR
Interesting. One small problem: I think the FogMate slightly randomized the timing so that you couldn't "sync up" with another vessel and never hear each other until it was too late. I don't remember seeing this as a requirement in the Nav Rules, but it seems like a good idea.
I've been playing around with ESPHome, and you could do something similar with an ESP8266 board and a relay. I think they sell boards with that combination already installed. It would be overkill, but even after buying the power supply and a small project box to house it, it would be a lot cheaper than the alternatives posted here.