You'll find the binding has hairline cracks in it where it bends round the body. The tighter the radius, the more cracks you get.
Stain tends to get in the cracks, spirit based more so than water based, and can be almost impossible to get out. So masking is strongly advised. You can use pinstriping tape (3M do good 3mm and 6mm wide vinyl tapes) or you can paint on rubber masking compound. There are other methods that people here use that I've forgotten.
Just be aware that the stretchy vinyl tape tends to pull away in concave curves, so I tend to use vinyl tape on the top (as it follows curves so well) and a paper tape on the sides.
You may need to sand or scape the binding to clean things up afterwards, but that's fairly easy to do.
It is normal to clear coat over the binding, but some people leave it as it is. I always clear coat it.
I had to paint all the binding on my ES1 as the stain in the cracks was so bad. It wasn't just a case of touching a few bits up. That's why I now mask the binding.
I buy modeller's masking tape that comes in a set of different widths, from thin to fairly thick. I use this for masking the side binding and also for masking fretboards between frets. Far easier than cutting down wide masking tape.
Did these too. Oooooooo that green........ The red came out more brown than anything. (No pic for that one). I like the blue, but the black dye didn't accentuate the grain like I'd hoped. It might be the sample board grain. All of them are basswood ply. Got as close to the body material as I could. I'll try some clearcoats next. See how they react to the water-base dye. Having some fun here.
Whoa! Dry fit is a bit rough there. Suppose I should dryfit the bridge and see how to adjust the pocket. The bottom is VERY rough. I think the burred up grain needs to be smoothed out, but need to make sure the neck angle is good for the action. I'll start by smooooothing out the bottom of the pocket.
Think I'm going to flatten that surface on the nect to match the body. It has about .05" material that needs to be removed, moving the neck closer to the bridge. Not much I can do about the depth of the pocket. Maybe glue a shim in there? The gap is about .05". That's a lot of glue.
I don't see any inlays like mine on here anywhere........
I keep solving my own problems here. Lol. Turns out, the action would be about correct with the neck right in the middle of the overall play. What would I fill the gaps with after the neck gets glued? It still has the huge gap in the bottom of the pocket.
The neck inlay seems to be from an ES-3 (not currently for sale on the site), not the top diamond tooth inlay the GR-1SF should have. Here's the neck and body from my ES-3 when it arrived. Apart from the cutaway style and a few hole locations. they are very similar kits.
The GR-1SF neck's headstock should come with the two rounded 'scrolls' on the end, as in this PBG website picture of the kit.
If you haven't got that, then you may well have been sent the wrong neck for the body. If so, it looks like you may well need a new kit.
Whilst you have a lot of side area for gluing on the neck, the bottom the heel to the body joint is the most important one as that's the only part you can really clamp together for a strong joint. With that big a gap between the heel and the body, I wonder if any of that heel is touching the bottom of the pocket?
I'd also be looking at checking the neck angle,as it seems if you get the neck sitting flush to the top, then you get a gap between the heel and the side of the body. If you have it so there's no gap between the heel and the body, you'll end up with a gap between the neck and the top of the body. Which means that the neck angle can vary significantly. On my (and others) ES-3, the neck angle is too shallow and I cant get the bridge low enough for a good action. I've replaced the bridge with a lower one and tried filing things away, but still no luck.
So I'd straighten the neck so it's flat, run a straight edge along it and see where the end of the straight edge ends up where the bridge will sit. See how much of a gap you've got there and will the bridge fit in at its lowest setting (allowing for post insert rims etc)? If the bridge does see-saw, then does the neck need to be pointing up or down in order to get the bridge in the space under the ruler's edge.
If the angle looks OK, then you could glue layers of veneer to the bottom of the pocket to fill in any gap between the heel and the pocket bottom. I'd shine a light through the gap to see if the gap goes all the way through or not.
I tend to fill small cracks/gaps with a filler I've tinted with artists acrylics to to match the finish. But the current gap by the heel cap is pretty large, so if that still exists (or it's filled with a couple of layers of veneer that look ugly), then other people have added an extra block of wood as an extra heel cap to cover the join. It could be basswood to match the body, or it could be a dark wood to provide a contrast.
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The red came out more brown than anything. (No pic for that one). I like the blue, but the black dye didn't accentuate the grain like I'd hoped. It might be the sample board grain. All of them are basswood ply. Got as close to the body material as I could. I'll try some clearcoats next. See how they react to the water-base dye. Having some fun here. 
