The live side is where the procedure begins, therefore you put yourself on the live side to commence the procedure. You can go around in the overhead in accordance with Rule 12 as many times as you like before commencing the procedure and whilst trying to fathom out the content of the signal square and work out where you are going to go. An "overhead join" commenced on the Dead side is actually a Crosswind Join because you are not complying with the Standard procedure and the place you join the circuit is on the Crosswind leg.
That's your assertion, Whopity. But the only guidance on the subject, which is not even regulatory in itself, depicts only one arrival direction. How that procedure generalises to other arrival directions is open to interpretation.
But I do feel that in a warming world of £2 Avgas, flying around in circles more than absolutely necessary is something of a waste.