The side not being tuned needs to be how it would be in normal operation. This means if the side not being driven (tuned) has 20 feet of coax running to the "switch" panel, and that coax is unterminated when not in use, then that's exactly how it needs to be when you tune the other side.
When George said to keep them both connected, I think he assumed you would be connecting your analyzer at the shack end of each of those cables.
If you are tuning by SWR alone, this should work ok, but if you are measuring the feed point impedance, then you want to OSL calibrate to the end of those aligator clips. The ideal length for a VNA test cable is 1/2λ, not 1/4λ. I would recommend the OSL calibration anyhow.
If you ever change to a real coax switch, you may need to redo this tuning process because most coax switches short the unselected port (which is opposite to what you have now with the unused coax being open) and could significantly affect the tuning.