For guitar kits, the veneer is 0.6mm most of the time. This sounds like nothing, but if you are careful, it can take quite a bit of sanding.
I'd also try goof off/acetone first. But if the veneer is so porous that glue squeezed right through it, keep in mind that the acetone will also probably creep right through and may lead to lifting/bubbling. So it may be better to do several lighter treatments than trying to get it off all at once.
I have so far been quite successful with acetone in regards to removing glue stains, but it can take 4-5 treatments until it's really gone. I also prefer rubbing with cotton swabs and an old tooth brush instead of brass bristles. The brass bristles can damage the veneer surface so it stands out when staining.