  A key uncertainty in interpreting observations of bimodal merging galaxy
clusters is the unknown angle between the subcluster separation vector and the
plane of the sky. We present a new method for constraining this key parameter.
We find analogs of observed systems in cosmological n-body simulations and
quantify their likelihood of matching the observed projected separation and
relative radial velocities between subclusters, as a function of viewing angle.
We derive constraints on the viewing angle of many observed bimodal mergers
including the Bullet Cluster (1E 0657-558) and El Gordo (ACT-CL J0102-4915). We
also present more generic constraints as a function of projected separation and
relative radial velocity, which can be used to assess additional clusters as
information about them becomes available. The constraints from these two
observables alone are weak (typically $\gtrsim 70-75^\circ$ at 68\% confidence
and $\gtrsim 55-60^\circ$ at 95\% confidence) but incorporate much more
cosmological context than the classical timing argument, marginalizing over
many realizations of substructure, peculiar velocities, and so on. Compared to
the MCMAC code, which implements the timing argument on NFW halos, our
constraints generally predict subcluster separation vectors closer to the plane
of the sky. This is because in realistic mergers the subcluster velocity
vectors are not entirely parallel to the separation vector (i.e, the mergers
are not perfectly head-on). As a result, observation of a nonzero relative
radial velocity does not exclude a separation vector in the plane of the sky,
as it does in the head-on timing argument employed by MCMAC.
