Question about input controls on Sprout

Hello! I have a Sprout and am integrating it into a raspberry pi controlled audio system.

I’d like the raspberry to be able to control which input is used on the Sprout (vinyl, bluetooth, digital) and so plan is to remove the input selector knob board from the 12-connector header and replace it with solid-state relays controlled by the GPIO pins.

So I took a look - the 12-connector cable is attached to a 21-pin 4-position rotation switch. I’m a bit flummoxed figuring out how to replicate the selects - is it possible to get some info on the rotation switch used in the Sprout?

Many thanks.