Sorry, I had not read your last post when I made my post about the enhanced linking mode needing an extra 4 second press.
I don’t have an ISY so consider that when evaluating this. When you say you put the ISY in linking mode, it sounds like the ISY would be listening for responder devices linking up to the ISY controller. Putting the EZIO6I into linking mode does put it in a linking mode listening for responder devices. Having two devices in controller linking mode, each listening for responder devices would not result in the ISY and the EZIO6I being linked together. In fact the EZIO6I has no outputs to act as responders. I may just not understand the terminology used by the ISY.
I am familiar with linking Insteon devices together however. Putting the 6I into linking mode, with the end result the LED is blinking once per second, pressing the top paddle on the SwitchLinc for 10 seconds should have caused the SwitchLinc to become a responder to the 6I Input selected during the link mode setup. A 4 second Set button press on the 6I may be needed to complete the linking process at the 6I if the enhanced linking feature is present in the 6I. If you cannot do a basic responder link from a SwitchLinc to the 6I, I would not worry about trying to connect the 6I to the ISY. In fact, the ISY should not be in linking mode during this process as the SwitchLinc enroll message might be absorbed by the ISY. Try linking the Switchlinc to the EZIO6I without the ISY being in the picture. There is always the possibility that the 6I is on one electrical phase and the SwitchLinc is on the other electrical phase, with the cross phase coupling not working, but that is pretty far afield. Would think you would be having other problems besides the 6I linking problem if there was a cross phase coupling issue.