Toyota Repair: sticking brake caliper piston Toyota Corolla, brake caliper piston, piston rod

Question
Is it possible to free up a sticking brake caliper piston rod
with a small amount of penetrating oil applied judiciously?

If not, is there another way to free it up so that it does not contribute to
drag and wear?

Answer
Calipers usually stick due to rust which means there is some moisture either from external sources of within the brake fluid, to answer your question yes the pistons can be freed up using penetrating oil, petroleum based oils can deform the rubber piston seals so at that time I would recommend replacing the o-ring seals in the caliper, since I'm not sure what year and model this is I will also make a general recommendation to clean and lubricate all moving parts such as sliding pins and brake pad contact areas, I hope this answers your question if not please let me know.