IIRC Godox TT350 is optically controlled off camera only, hence should be on slave and Auto mode, not TTL supported.
alcelc has not remembered correctly. The TT350, like your larger TT685ii, has built in radio that can either transmit (TX) or receive (RX). I have both units in Flashpoint/Nikon flavor. Either one can be in the hot-shoe and the other off-camera. I bought the TT350 specifically to have a small on-camera fill light while triggering larger off-camera lights.
Both your light have the "S1" and "S2" optical remote modes which is what alcelc is remembering.
Does "optical" imply it has to be in the line of sight?
FYI optical triggering can work without line of sight in moderate-sized rooms provided you have reflective walls/ceiling to disperse the light from the on-camera flash. Line of sight is better of course and required outside, but if the ambient is high your range may be limited.
My intent was to use the built in radio trigger mechanism (whatever it's called).
Agreed you should use the radio triggering, but if you are like me the issue becomes "how do I make the radio magic work".
I find it difficult to get my units configured the way I want especially if I haven't used them recently.