Smartifying Christmas Holiday Tree w/ 12v combined power/signal

I have a Home Accents Christmas Holiday tree from Home Depot (like that I’d like to control with HA. The tree supports multiple modes like: solid white, solid colors, pulsing colors, pulsing white, etc.

The foot switch has a single button to cycle through modes. The output from the switch (input to tree) is 2 wires. Foot switch has a number of discrete components, no obvious microcontroller.

The control/power signal varies between appx 9v and 13v on my cheap, slow-refresh multimeter.

How can I go about decoding the signal? I am aware of cheap usb logic analyzers, but they run at 5v. I’m not sure how to deal with the possible 14ish volts.

And then I’ll have to figure out how to make my own driver, probably out of an ESP8266 or ESP32.

I’m not that interested in something that would monitor/interact with the tree, like a power monitor or color detector or button pusher.