The lash up works. I can control a 120 VAC lamp with the dimmer
triggering the external triac. So at least it triggers on 120.

Before it goes into the range, I need some mounting washers for the
triac. These are bolted to a bare heatsink and I'd rather insulate
the triac than insulate the heatsink.

Still want to tinker a bit to see if the bare, out of the box, dimmer
can be made to work the triac with only the two wires they supply.
--

Wire it up on 240 powering a couple of 200-300W incandescent bulbs in
series, if that works then it should work fine with the burner.