Are you referring to the red ink in general or specific to Gypsy? There are a number of ladies who signed in red back in the day. Betty Grable for instance. All I can go by is the signature which looks quite comparable.
It looks OK to me. You have to remember that vintage stuff is often signed long after the fact. I have a couple double weight paper prints from the late 40s that Sharyn Moffett signed a couple years ago in black sharpie. It appears to look like ballpoint but that is well within her lifetime since she didn't die until 1970.