A traditional way of attaching hanging objects to masonry was to drill a hole, bang in a wooden dowel, and then fasten into the dowel with a screw or nail.
In your case this could help reduce the accuracy needed in the holes in the brick. I find drilling accurate masonry holes challenging because the base material is often of varied composition and that causes drill wandering. But if you use a largish dowel then you don't have to be as accurate, and have some wiggle room to position the actual fastener (screw, etc.)
Depending on how closely the dowel stock fits the hole you might need to either shim it or sand it down. Ideally you'll start with a larger dowel, sanded to a taper on one end, and then drive it in hard.
Alternatively wooden wedges could work nearly as well, as long as there is enough material to put a screw in.
(Even common plastic plugs offer a small amount of adjustment, but I find often not enough).
If the hole ends up a little bit larger than the dowel, you probably could also glue the dowel in place with construction adhesive (that is meant for masonry). If well glued, when dry that should be pretty solid too (but I would prefer a tight mechanical fit over glue).
As for measuring the hole location, I would make a cardboard template with small holes made to compare against the mirror or other object, and to use the same holes to mark off on the wall.