Page signatures like this are largely out of my league. They are just too easily done in my opinion. My initial opinion would be No, but wait for others. I definetly could be wrong
I would say fake, but it does have some of the things fakers miss correct. Most real Jimmy autos have the up part of the J slightly flatter than the rest of the curve. Its a close run thing elsewhere on this. the downstrokes should be parallel or slightly tapering to each other, which these are. I do have a genuine JP auto from the Coverdale Page promo photos, but the pen used is pretty thick, which wouldn't help your comparison. Going by feel I would say no though.
Not a page expert but if I was to compare mine to the one above it don't look the same hand writing if you look at how he starts and ends each section etc. But thats just comparing it to one so dont mean nothing i guess.