No, no elmer's glue... there's an industrial glue that is used on the wood, put on by a hand roller and then applied to the formica backing aswell. It takes about 5-10 minutes of air drying to cure the glue, then the formica is applied to the countertop and hand pressed with a weight covered in a soft cloth to remove any airpockets. Then it's routed twice.
I work at a kitchen cabnit place and do formica countertops and everything else associated with it. If you need glue, I got it for you. We'll make arrangements for pickup if you want it. Free of course for a MR member.
1st Scarr the area with a fine razor, that needs to be removed. Box cutter works well or a utility knife. The latter is better.
2. Paint thinner, small brush, industrial glue, and putty knife.
3. Take the brush, dip in paint thinner and apply to the area that was cut and scarred... wait a minute and repeat. Your trying to get the paint thinner into the grooves where you cut so the thinner can act as a releasing agent on the glue. Usinging the putty knife you try and wedge it into the cut you've made and try lifting the formica up off the countertop. While your doing that your wedging the brush underneath aswell releasing the rest of the formica. Do it slowly as not to break it into pieces. Now that it's off you clean off the glue from the surface area where only the wood is now exposed. You'll see that its brown but not burnt unless it was a decent fire that charred the wood. Apply glue to the wood and the back of the new cutout formica and wait 5-10 minutes. Curing time. Then apply it to the countertop. SUse a heavy object wrapped in a soft cloth to press onto the area and rub in. Remove any excess glue around the edges with a cloth dipped in paint thinner and your done.. 20 minutes tops