Two stages Two servers One net?

Have two Hog 3 pc servers running 3.19 one on each of two stages with two different static IP addresses. I bounce a hog 3 console and a wireless tablet between the stages to log into the individual server network on each stage for programming.

I'm looking for a way to connect the two servers running two different shows to the same network so I can log onto either show from either stage with the console and tablet.

If I connect the two stage networks with a cat 5 cable between the two switches in the server racks will both servers show up on my log in screen? I have the feeling it's more complicated than that.
Related