I don't really know if that repair would work, Art.
I thought about trying to fill the joint with glue and sanding dust, but decided that the joint looked bad enough that I would do a proper repair.
I think the superglue would leach into the wood causing a stain. This guitar is not being painted, so clean wood work is a must.
I got the router table set up as a jointer and straightened the edges of both the neck, the body, and the headstock.
This is my set up. I slip a couple strip of very thin cardboard behind the out-feed side of the router table fence.
Although there is a bearing on the bit, I only use it to help get the fence set correctly.
I put a straight edge against the out-feed side, and move the fence so the straight edge just touches the bearing.
Then I raise the bit so that only the cutting edges are contacting the wood.
The cardboard is not quite 1/64" thick, so I get a pretty thin cut.
Here, the sides are set close to the bit.
After repairing the joints, the body is glued up again.
And the headstock too.

I need your help. I can't possibly make all the mistakes myself!