GRRRRRRRRRR Firefox has a way of getting an error on T-man page right after I write 5 paragraphs!
WHAT I WAS SAYING was, you need some benzene solvent cleaner.
This stuff is hard to get these days as it causes cancer and even the fumes are highly toxic. But it was used on a daily basis in all sorts of cleaners of yesteryear.
USE THICK GLOVES the type you can buy at Home Depot that are heavy-duty. My father has spots of skin cancer on his hands and arms because he used to clean aircraft parts with it while he was in the Air Force, so that gives you an idea about how seriuos it is.
Limit your exposure, just do it outside, a few bits at a time. Every day work out about 3 spots of gum, and quit.
You need ventilation! Do it when there's a breeze.
Just dab some of the solvent on a folded paper towel, and pinch the fur and make a pulling motion. It should come right out of the fur. Don't rub it, just pinch and pull.
You can get benzene solvent cleaners at auto parts stores, and probably home construction supply stores. Try not to get it on the hide, just pull the gum off the hairs.
I got this information from a book called Tan Your Hide!, and this benzene stuff was the only thing that could remove the fir tree sap from my car.