@Ukdavewood you are right, I believe that the one in the A1 Mini is the 3mm pitch between pins. The one I just ordered (https://a.co/d/coCHUgQ, $8 at Amazon) is shorter than the one used by BL, but it will have to do since the shop lists on the web site but doesn’t fulfill orders for the BL branded one.
Thanks for pointing that out!
EDIT: Correction: the US shop changes the status to “Fulfilled” when it creates the shipping label but the actual shipping may take a long time to happen (cable is on its fourth day of this limbo). I guess that way the stats for the shop look good even if customer satisfaction goes down?
OK. Short answer to the original question: the 4-pin AMS Lite cable IS NOT a standard Molex 4-pin - For whatever reason, BL assigns the pins on both ends in a non-standard way.
How do I know? The 4-pin Molex cable, when installed, ended up on the printer and the AMS Lite not connecting after handshake, whereas the original BL cable (which I got two weeks+ after I started my search ) does indeed work.