We demonstrate that second-harmonic generation (SHG) from arrays of non-centrosymmetric T-shaped gold nanodimers with a nanogap arises from asymmetry in the local fundamental field distribution and is not related strictly to nanogap size. Calculations show that the local field contains orthogonal polarization components not present in the exciting field, which yield the dominant SHG response. The strongest SHG responses occur through the local surface susceptibility of the particles for a fundamental field distributed asymmetrically at the particle perimeters. Weak responses result from more symmetric distributions despite high field enhancement in the nanogap. Nearly constant field enhancement persists for relatively large nanogap sizes.