Machinbird, the ACARS antenna is, apparently, a patch style antenna with no "gimbles" as such. It's electronically steered with a very wide beamwidth. (50 to 90 degrees) It can probably be steered to within 15 degrees to 20 degrees of the antenna's plane and, of course, all the way up to normal to the antenna's plane.
What I don't know is whether the antenna is operated open loop off aircraft navigation data or closed loop with a servo. Given the wide beamwidth I suspect the antenna is simply steered off basic aircraft navigation data and the (fairly well) known satellite position.
We discussed this back in the old thread. I don't remember enough of it off the top of my head to be sure on details. But I do believe a 50 degree bank would have put the aircraft between the antenna and the satellite which was off to the West of the aircraft by a significant amount. Digging back to the original discussion should dig out the details of the antenna. I remember a posting that pointed to the manufacturer's data sheet.
{^_^}