IMHO that's too deep a gouge to attempt to patch without using a filler. Gelcoat is thin and isn't designed to handle loading or depth (material thickness). If that were a scar on my boat, I would have removed the loose chips if not used a Dremel on it, wet out matting with thinned penetrating epoxy, would have scratched that epoxy layer up good, then added Formula 27 to sub-flush, and then would use gelcoat as the final finish layer.
PVA = 'Polyvinyl Alcohol', a mold release product, used like stated above to seal off gelcoat for a full cure, as gelcoat without wax needs an anerobic environment.
Sanding: When G-Jim above said sand above, he meant to say WET sanding. Use various grits, I start at or around 200, depeding on the locale and may go up as high as 1000 or more. When wet sanding, the paper and block should be in the water being rinsed MORE than it is on the gelcoat sanding, at least for the finer grits.