The (type A) Hecke algebra $H_n(q)$ is a certain module over $\mathbb Z[q^{1/2},q^{-1/2}]$ which is a deformation of the group algebra of the symmetric group. The $\mathbb Z[q^{1/2},q^{-1/2}]$-module of its trace functions has rank equal to the number of integer partitions of $n$, and has bases which are natural deformations of those of the symmetric group algebra trace module. While no known closed formulas give the evaluation of these traces at the natural basis elements of $H_n(q)$, or at the Kazhdan-Lusztig basis, we present a combinatorial formula for the evaulation of induced sign character traces at a certain wiring diagram basis of $H_n(q)$.