Given an open book decomposition (Σ,τ) of a three manifold Y , Thurston and Winkelnkemper [TW] construct a speciﬁc contact form a on Y . Given a spin-c Dirac operator D on Y , the contact form naturally associates a one parameter family of Dirac operators Dr = D− ir 2 cl(a) for r ≥ 0. When r >> 1, we prove that the spectrum of Dr = D0 − ir 2 cl(a) within [−1 2r 1 2 , 1 2r 1 2 ] are almost uniformly distributed. With the result in Part I [Ts1], it implies that the subleading order term of the spectral ﬂow from D0 to Dr is of order r(logr) 9 2 . Besides the interests of the spectral ﬂow, the method of this paper provide a tool to analyze the Dirac operator on an open book decomposition.