you wire the Beamswork power brick to the TC-420
Then wire the output from the TC-420 to the head..
If you don't want to wreck anything, just get matching plugs.
So, just to follow up on this and ask a possibly silly question (I'm a chemist, not an EE), could I simply buy an extension like this
and wire it onto the TC420, then use it inline between the power supply and light without actually having to mod the light at all? Seems pretty simple, but I have found that when it seems this straight forward it is because I am doing it wrong.
“Science, my lad, is made up of mistakes, but they are mistakes which it is useful to make, because they lead little by little to the truth.” -Jules Verne