Accreting supermassive binary black holes (SMBBHs) are potential multi-messenger sources because they emit both gravitational wave and electromagnetic (EM) radiation. Past work has shown that their EM output may be periodically modulated by an asymmetric density distribution in the circumbinary disk, often called an “overdensity” or “lump;” this modulation could possibly be used to identify a source as a binary. We explore the sensitivity of the overdensity to SMBBH mass ratio and magnetic ﬂux through the accretion disk. We ﬁnd that the relative amplitude of the overdensity and its associated EM periodic signal both degrade with diminishing mass ratio, vanishing altogether somewhere between 1:2 and 1:5. Greater magnetization also weakens the lump and any modulation of the light output. We develop a model to describe how lump formation results from internal stress degrading faster in the lump region than it can be rejuvenated through accretion inﬂow, and predicts a threshold value in speciﬁc internal stress below which lump formation should occur and which all our lump-forming simulations satisfy. Thus, detection of such a modulation would provide a constraint on both mass-ratio and magnetic ﬂux piercing the accretion ﬂow.