While Faceware Live and LIVE FACE both have IP address options, Faceware Realtime only shows "Auto", and I cannot connect to a second computer running the application.

How do you do this?

I don't think you can.  IIRC, Faceware is only allowed on one computer (and moving it from one to another is a royal PITA).

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Alienware Aurora R16, Win 11, i9-149000KF, 3.20GHz CPU, 64GB RAM, RTX 4090 (24GB), Samsung 870 Pro 8TB, Gen3 MVNe M-2 SSD, 4TBx2, 39" Alienware Widescreen Monitor
Mike "ex-genius" Kelley

Not moving Faceware to another computer. Streaming the data from the Faceware computer to the iClone/Motion LIVE computer.

It is supposed to be an option, but the UI has changed:
https://manual.reallusion.com/Facial_Mocap_for_Faceware_Plug_in/ENU/Content/iClone_7/Pro_7.0/29_Plug_in/Facial_Mocap_for_Faceware/Adding_and_Deleting_Servers.htm

You might have to contact support then (fill out a trouble ticket).

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Alienware Aurora R16, Win 11, i9-149000KF, 3.20GHz CPU, 64GB RAM, RTX 4090 (24GB), Samsung 870 Pro 8TB, Gen3 MVNe M-2 SSD, 4TBx2, 39" Alienware Widescreen Monitor
Mike "ex-genius" Kelley