Connecting an external control to a DPDT switch
Looking at th PCB those 2 DPDT switches are being used as SPST ones - one pin (the middle one) is wired to +V, the other is connected to an input on a chip with a pulldown resistor to ground (R6/10).

If the switches are off then the pin furthest from the panel will be pulled down by the resistor to ground - you could then drive it externally (run that pin and ground to the external controller.

Some caveats: if you accidentally turn the switch on bad stuff could happen - best to drive the signal through a small diode for protection - you also need to be careful about voltages - don't drive the circuit from something with a higher voltage than expected (perhaps snarf the power from that other pin assuming it's 5v)