A ball mount device, formed on a rigid non-metallic frame having an upright columnar stem portion projected from a circular transverse base portion, and an enlarged connector core on the upright stem portion distal of the base portion. A first elastomeric material is molded over the connector core distal of the base portion and forms a smooth part-spherical outer surface. A second elastomeric material is molded over the base portion and forms a pliantly conformable outer skirt portion extending outwardly thereof with a smooth and substantially flat and circular outer surface opposite from the stem portion. A pressure sensitive adhesive is provided on the outer surface of the elastomeric material coating the base portion for adhering the ball mount device to a mounting surface that is external of the ball mount device.