Seal Cement is the glue you want for seams.

McNett also makes the Aquaseal urethane cement, but that sucks for building things from neoprene. The Aquaseal is more for coating kneepads or gloves for grip or abrasion, or sealing drysuit seams.

The old Henderson Gold Core wetsuits and similar,(gold or silver skin on one side) are glued and then stitched on the nylon side of the fabric. The blindstitching only goes partway through the neoprene. So a tail can be made the same way.