The Neph came over and we probed the RC circuit with the analog multimeter that I purchased from Radio Shack. I was astonished to find that the voltage on the high side of the push button wasn’t even a single volt. Actually it’s so low that a diode across p1 and p2 won’t even light up.
I’ve come up with the idea shown for an Arduino/RC board interface circuit. The resistor values (TBD) are such that one is four times greater than the other. Then, when the Arduino digital output (pin TBD) goes high, it generates 1 volt at p2. Counterintuitively, that is the equivalent of the button being unpushed.
To simulate the button being pushed, the Arduino digital output has to go to low — ie, ground. The RC circuit is operating on two AA batteries, so I’m pretty sure the current won’t burn out the Arduino. Indeed, other way around, I should choose resistor values so that the Arduino doesn’t burn out the RC circuit. Next time.
It also occurs to me that while transistors switches probably won’t work here because of the low voltage, a mechanical relay could. So I should look for some relays on the Internet too.