With cars that have been stored, the actual e-brake cable can seize in the steel jacket. Check to see both the inner cables move back & forth when the handle is pulled. But mostly it's varnish causing a piston or two to stick in the 'on' position at either front or back (or both). I've had cars with completely plugged bleeder screws that needed to be drilled out to bleed the calipers! Disassembly and thorough cleaning is the fix and while you're in there, it's smart to rebuild the caliper(s). After all, it could be 50 years since anyone dug around in them and nothing lasts forever. Sticking brakes are not safe!
There have been several illustrated articles in POCA Newsletters over the decades on how this is properly done. Mike Daily's website likely also has directions. Vendors sell kits for both ends of the car (two brakes) or replacement calipers with your cores, but be warned: this is one of the dirtiest most miserable, sloppy jobs on your car and it will take a full weekend (at very low cost) for an inexperienced owner to do correctly- if nothing is broken or lost. It's quite possible to do it wrong, as well.... Rumor has it that one such owner wound up under a semi-trailer during his check ride. Two experienced guys (with kits, new fluid and the proper tools) can and have correctly fixed all 4 calipers in an afternoon, during a yearly Chapter Tech session. Just another reason to not be a lone wolf owner....