Extensive grand canonical Monte Carlo simulations have been performed for the hard-core square-well fluid with interaction range b=1.5 sigma. The critical exponent for the correlation length has been estimated in an unbiased fashion as nu= 0.63+/-0.03 via finite-size extrapolations, of the extrema of properties measured along specially constructed, asymptotically critical loci that represent pseudosymmetry axes. The subsequent location of the critical point achieves a precision of five parts in 10(4) for T-c and about 0.3% for the critical density rho (c). The effective exponents gamma (+)(eff) and beta (eff) indicate Ising-type critical-point values to within 2% and 5.6%, respectively, convincingly distinguishing the universality class from the ''nearby'' XY and n = 0 (self-avoiding walk classes. Simulations of the heat capacity C-V(T,rho) and d(2)p(sigma)/dT(2), where p(sigma) is the vapor pressure below T-c, suggest a negative but small Yang-Yang anomaly, i.e., a specific-heat-like divergence in the corresponding chemical potential derivative (d(2)mu (sigma)/dT(2)) that requires a revision of the standard asymptotic scaling description of asymmetric fluids.