Get some maple veneer, cut it roughly to size, then glue and clamp it to the side of the neck pocket. Wait 24 hours, then trim the excess down to size. Then sand back in the areas where its tight until the neck fits snugly. I've had to do it to both sides of the neck pocket on my ESB-4 kit. If you can, I'd glue it on the other side of the neck pocket, so it's away from you and you are less likely to notice it (though that depends on your proposed finish and whether that is likely to cover up all signs of it).
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Put masking tape right along the edge of the pocket, so that if any glue does squeeze out when you clamp it, it doesn't go on the top. Wipe the excess glue off wherever you see it, but it's best to avoid getting any on the top or sides where it may affect the ability of the wood to absorb stain or other finish.