Refurbished my rear calipers, both due to sticking handbrakes.
Problem was the shaft with the cable arm wouldnt return to fully off position, even with the big spring in place, and cables disconnected.
It is possible to flush the arms with penetrating oil, by squirting under the seal, but once they get to this condition they need stripping, cleaning and greasing.
One refurbished no problems, but the other had damaged needle bearings (pitted and missing rollers), which spares are not available, so i had to replace this one with a 2nd Hand caliper
Cleaned, inspected and painted and all OK again.
The actual auto adjustment mechanism rarely gives trouble, but you need to dismantle it to get the actuating mechanism out to clean and inspect.
Relatively easy if you get the "special" circlip pliers.
I would recommend getting a pair of used calipers, refurb these, and replace them, then refurb the ones removed.
Then you can do the work at your leisure.