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Will X4, the center tap, become the neutral? And should this then be bonded with the ground in one, and only one, location? What did you mean by "NOT a standard neutral for the 3 phase"?
The center tap on one winding becomes the ground point for the secondary, yes. It gets grounded to whatever NEC ground you have, building steel, the green wire of the 480 supply, a etc. Yes, pick ONE to connect it to, and bond THAT to the distribution breaker box for the transformer (if any).
It is NOT the neutral for the 3 phase
because it does not have the same voltage to all the wires. It will be the neutral for the two wires at the ends of the tapped winding, with 120V to each, but will be about 200V from the "high leg" or "stinger" leg, which is conventionally wired with orange wire or ID to show what it is.
The option of a lighting tap exists for 240V 3 phase, but 208V naturally has a normal neutral, with 120V from that neutral to all phase wires. If you have the option of using 208, that could be a good move, because it is simple with less to remember.
But 208 is not always acceptable. Most 240V motors don't really "like it", although they may be able to accept it. Higher current for the same power, and less power than marked if you stay within the marked current. It's 13% less voltage than nominal 240V.