How can I use an Arduino to simulate button presses on this PCB
The switch does not provide power to the circuit it is connected to. It merely connects two points together (or not).

It appears that one side of the switch in question is tied to the ground plane of the board. The switch is therefore connecting its other terminal to ground when it is pressed.

You could simulate this easily with a transistor; for example, a small logic-level N-channel MOSFET would work nicely.







simulate this circuit &ndash; Schematic created using CircuitLab

The ground of the Arduino must be connected to the ground of the target PCB, but they don't necessarily need to share any other connections.