For a critical binary liquid mixture where the surface tension difference between the two components is very large, the component with the lowest surface tension completely saturates the liquid-vapor surface. The variation in the local volume fraction v(z), with depth z into the liquid mixture, is described by a universal surface scaling function P(+/-)equivalent toP(+/-)(z/xi(+/-)), which takes differing forms in the one- (+) and two-phase (-) regions, where xi represents the bulk correlation length. Carpenter [Phys. Rev. E 59, 5655 (1999); 61, 532 (2000)] determined P+/- using the ellipsometric critical adsorption data of four different critical binary liquid mixtures. A deficiency of this prior study was that each of the liquid mixtures possessed at least one polar component, which could have generated distortions in the function P+/-(z/xi(+/-)). In this publication, we demonstrate that P+/-, determined in the previous study, provides an excellent description of the nonpolar critical binary liquid mixture 1,1,2,2-tetrabromoethane+n-dodecane.