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We obtained four pointings of over 100 ks each of the well-studied Wolf-Rayet star WR 6 with the XMM-Newton satellite. With a first paper emphasizing the results of spectral analysis, this follow-up highlights the X-ray variability clearly detected in all four pointings. However, phased light curves fail to confirm obvious cyclic behavior on the well-established 3.766 d period widely found at longer wavelengths. The data are of such quality that we were able to conduct a search for "event clustering" in the arrival times of X-ray photons. However, we fail to detect any such clustering. One possibility is that X-rays are generated in a stationary shock structure. In this context we favor a co-rotating interaction region (CIR) and present a phenomenological model for X-rays from a CIR structure. We show that a CIR has the potential to account simultaneously for the X-ray variability and constraints provided by the spectral analysis. Ultimately, the viability of the CIR model will require both intermittent long-term X-ray monitoring of WR 6 and better physical models of CIR X-ray production at large radii in stellar winds.