Sorry for the ambiguity. I try to describe the problem in as abstract a term as possible, to avoid boring people with unnecessary details, but I see that's usually not helpful. The signal is from a welder, through a switch on the welder's torch. The switch is used to activate the arc. The welder is putting 2.7 volts on one pin, the switch is normally-open. Presumably, the welder has a voltage threshold over which it will consider the pin to be "high", but I don't know exactly what that is. I don't have a proper DC power source to put direct, controlled voltage on the pin to test it out. Maybe I could put a 10k pot on a 5 volt digital output set to HIGH and raise the pot until the welder trips, then measure the voltage on the line.
The intent of the device that I'm building is to act as an intermediary between the welder's remote inputs (torch and pedal) to cause the welder to act in more sophisticated ways. But the simplest thing the device has to do is to be able to pass inputs through transparently. So when the Arduino detects that the torch switch is pressed, it needs to connect the equivalent two pins on the welder's input.
EDIT to add: just to be clear, the switch is used to activate the arc, but the switch is NOT carrying the full welding current. The switch circuit is something like 2.7 volts at 4 mA.