It's mainly the taper holding it, the rust just adds a little.
I'd make a U-shaped wedge and spacers, insert them between the stuck center and the tailstock spindle, strike sharply. Done.
Use the access to the end of the live center from the threaded end. Get the biggest soft steel rod that fits through the I.D. of the thread and hold it all together while you slam it on a solid, hard surface (anvil?), pin down. The live center should just pop out. When I say biggest rod that'll fit, get a piece of 1018 and turn a diameter to just fit in there and make it just a 1/2" (10-12mm) longer than the depth of hole. The bigger the better, I'd shoot for 3" diameter, 6" long. You need MASS.
BTW, most tailstock spindles have a slot where the tang of a mating Morse taper would land, enabling you to use a drift key to pound loose a stuck taper. After you get that out, lay the center and then a another device with the tang bext to and lay out where the slot on yours should be. Then mill one!
I'd make a U-shaped wedge and spacers, insert them between the stuck center and the tailstock spindle, strike sharply. Done.
Use the access to the end of the live center from the threaded end. Get the biggest soft steel rod that fits through the I.D. of the thread and hold it all together while you slam it on a solid, hard surface (anvil?), pin down. The live center should just pop out. When I say biggest rod that'll fit, get a piece of 1018 and turn a diameter to just fit in there and make it just a 1/2" (10-12mm) longer than the depth of hole. The bigger the better, I'd shoot for 3" diameter, 6" long. You need MASS.
BTW, most tailstock spindles have a slot where the tang of a mating Morse taper would land, enabling you to use a drift key to pound loose a stuck taper. After you get that out, lay the center and then a another device with the tang bext to and lay out where the slot on yours should be. Then mill one!