Incompleteness in the selection of variable stars can bias the observed period-color and period-amplitude distributions. To assess the completeness of our sample of rotation periods we conduct Monte Carlo simulations of the variable star selection process. We inject sinusoidal variations, and spot signals (generated using the model described in § \[sec:perunc\]) into the light curves of 1081 stars that pass the cuts used to select candidate cluster members discussed in § \[sec:rotsel\] but were not selected as variable stars. For each star we conduct 1000 simulations. For the sinusoid models we inject signals with random phases, periods uniformly distributed in logarithm between $0.1$ and $20.0~{\rm days}$ and semi-amplitudes uniformly distributed in logarithm between $1~{\rm mmag}$ and $0.1~{\rm mag}$. We attempt to recover the injected signals using the L-S algorithm in combination with the multi-harmonic AoV algorithm. An injected signal is considered to be recovered if it does not have a period falling within one of the rejected period bins discussed in Paper II, has a formal L-S false alarm probability logarithm that is less than $-150$ and if the N=1, 2 and 3 periods returned by AoV agree with one another to within $10\%$. To make the problem computationally feasible 