  We consider one-dimensional discrete Dirac models in vanishing random
environments. In a previous work [6], we showed that these models exhibit a
rich phase diagram in terms of their spectrum as a function of the rate of
decay of the random potential.
  This article is devoted to their spectral statistics. We show that the
rescaled spectrum converges to the clock process for fast decay and to the
Schr\"odinger/Sine processes from random matrix theory for critical decay. This
way, we recover all the regimes previously identified for the Anderson model in
a similar context [25]. Poisson statistics, which should appear in the model
with slow decay, are left as an open problem.
  The core of the proof consists in a suitable scaling limit for the Pr\"ufer
phase and monotonicity arguments, yielding an alternative to the approach of
[25]. For one of the models, we also obtain the scaling limit of the Pr\"ufer
radii and discuss the consequences for the limiting shape of the
eigenfunctions.
