While other materials will hold the box, my suggestion is to get a tube of NP-1, a urethane sealant available at most commercial roofing wholesalers.
Blow out all the dust possible first. Put as much NP-1 as possible between the box and the brick. Do not disturb it for a week. Then remount the fixture.
The NP-1 is available in colors. Once opened, it must be used within a couple of days as it will get too stiff to be applied with a caulking gun. There are other urethane sealants that are excellent but some are not stiff enough to stay in place when they are applied for this purpose.

I've had good luck just using gray concrete silicone. We tap in a shim or two first to hold the box firm then apply the silicone. The fixture can be installed immediately due to the shims holding the box. As a home owner however you have the luxury of waiting to install the fixture. Once the silicone dries it conforms to the uneven surfaces of the brick and the box, and that box will not come loose.

Thanks for the quick responses. Sounds like good suggestions. I believe these products both dry somewhat flexible after curing. So, would they be stiff enough to hold the junction box securely?

Applied as I described, the NP-1 will hold the box quite solidly.

If the box is like the ones in my house it has a mounting plate (wider than the box) on the back that sticks out to each side or to the top and bottom. When mounted in cement the plate extends into the mortar. Even though the mortar has broken loose, the plate may still be positioned behind a brick so that the box cannot come completely out. Adding some shims and the NP-1 should stabilize it enough to hold solidly.

Bruce

Thanks to all your suggestions, I did this as follows:

Used plastic shims as suggested, but instead of polyurethane or silicone caulking, used hydraulic cement to secure them in place. There was not enough space between the brick and junction box to worry about expansion of the material as it cures. I gently knocked the shims in and used my fingers to force a fairly thick mixture of the material around them. Seems very solid. and if something goes wrong I could drill or chip out this material, whereas PU caulking could be a problem to clean out.

I was concerned about the long curing time of some of the caulks (7-10 days) and cold weather was on the way. The mortar-like material cures in 1-2 days and has a fairly wide temperature tolerance.

Sorry to take so long to get back to report, but could not get to this job earlier.

Thanks all and happy holidays!