Suspensions of paramagnetic colloids are driven to phase separate and self-assemble in toggled magnetic fields. At field strengths above 575 A/m and toggle frequencies between 0.66 and 2 Hz, an initial gel-like, arrested network collapses into condensed, ellipsoidal aggregates. The evolution to this equilibrium structure occurs via a Rayleigh-Plateau instability. The toggle frequency ν determines the fluidity of the breakup process. At frequencies between 0.66 and 1.5 Hz, the suspension breaks up similar to a viscous, Newtonian fluid. At frequencies ν > 1.5 Hz, the network ruptures like a viscoplastic material. The field strength alters the onset time of the instability. A power law relationship emerges as the scaled frequency and field strength can be used to predict the onset of breakup. These results further aid in understanding the mechanics and dynamics of the phase separation process of suspensions of polarizable colloids in toggled external fields.