We consider a U(1) gauge theory on the five dimensional orbifold $\mathcal{M}_4\times S^1/Z_2$, where $A_5$ has even $Z_2$ parity. This leads to a light pseudoscalar degree of freedom $W(x)$ in the effective 4D theory below the compactification scale arising from a gauge-invariant brane-to-brane Wilson line. As noted by Arkani-Hamed et al in the non-supersymmetric $S^1$ case the 5D bulk gauge-invariance of the underlying theory together with the non-local nature of the Wilson line field leads...