Well I am no taxidermist, but I do know that they use pins to hold things down, thus foam forms
and a tanned hide is soft?
Can dampen the hair and then pin a piece of cardboard over the section, I would also think the plastic wrap or even an ace bandage can work, but it might flatten the hair all around too??
I would stop at a local shop and ask, seems like a simple issue
and or ask for a couple of there pins? They have a "T" head on them, to help hold pressure against parts of a mount!
Maybe even wet area, hold down with a piece of screen, and use a hair dryer , to dry it in correct way!??
good luck, let us know how it works out! Never know who else might need to know some day