This piece came with a large collection of Olivia prints and lithographs. Including other authenticated Bettie Page signed gilcee prints. To my best estimation, the signature is not part of the photo itself, so it does look like someone signed it.
The signature appears to be signed in felt tip pen like a sharpie. If this is the case, when you turn it in a light source it should appear to be on top of the gloss of the photo and look almost as if it changes color (picking up the light reflection.)
I ran another light over it, and it does appear to have distinctive markings that look like a pen stroke. It changed color slightly when I moved the light and it also appears to have like a "brush stroke" like appearance. Not sure if I am using the right term or not. I also have a book I am attempting to ascertain the authenticity of.
There was a receipt from Playboy, indicating a Bettie Page signed book. The only book I have found in the collection was the following:
This one is much more difficult to determine, since the pen used appears to be even more of a fine tip then a sharpie.