Trouble Using Arduino as a Timed SPDT switch

First time trying to use an Arduino and could use some help. I have a controller with a manual print button that I'm trying to automate on a regular time interval using my Nano.

The way it is wired now, there's a momentary switch with two leads that when not pressed has +5V across them. When pressed, the potential drops to 0V and it prints. It's a low current circuit so I figured I wouldn't need a relay to do the switching, as I know the pins on the Nano can handle up to 40mA.

I tried to repurpose the blink library example and am able to get the output on Pin 13 to loop +5V to 0V back to board ground, but when wired in-line to the circuit doesn't work as expected. Any help would be appreciated.

Did you connect the grounds of the Arduino and the printer?

The proper way to make the connection and not to worry about the grounds is to use an "opto-isolator". Google that. It is an LED and a transistor. Your Ardiuno turns on the LED and the transistor is turned on by the LED light, which switches the printer signal to ground, just like the mechanical switch does.