Paul in NJ
I would use liquid hide glue warmed and thinned a little with water. You probably do not need to clamp, just position the piece so gravity holds it in place. Hide glue pulls the joint together as it dries. It is reversible with some heat and moisture and can be re-glued again without removing all of the glue in the joint. Clean up with a little hot water. It takes stain unlike other glues. It is the first choice of restorers.
I bought a kit of dry pigments cheaply form Lee Valley that I use to touch up. A little pigment is mixed with a little shellac using a small artist brush. You can mix and match the pigments to get the right color. If you don't like the results, rub off with a rag dipped in alcohol.