We present an optical variability study of 44 newly identified blazar candidates behind the Magellanic Clouds, including 27 flat spectrum radio quasars (FSRQs) and 17 BL Lacertae objects (BL Lacs). All objects in the sample possess high photometric accuracy and irregularly sampled optical light curves (LCs) in I filter from the long-term monitoring conducted by the Optical Gravitational Lensing Experiment. We investigated the variability properties to look for blazar-like characteristics and to analyze the long-term behaviour. We analyzed the LCs with the Lomb-Scargle periodogram to construct power spectral densities (PSDs), found breaks for several objects, and linked them with accretion disk properties. In this way we constrained the black hole (BH) masses of 18 FSRQs to lie within the range $8.18leqlog (M_{rm BH}/M_odot)leq 10.84$, assuming a wide range of possible BH spins. By estimating the bolometric luminosities, we applied the fundamental plane of active galactic nuclei variability as an independent estimate, resulting in $8.4leqlog (M_{rm BH}/M_odot)leq 9.6$, with a mean error of 0.3. Many of the objects have very steep PSDs, with high frequency spectral index in the range $3-7$. An alternative attempt to classify the LCs was made using the Hurst exponent, $H$, and the $mathcal{A}-mathcal{T}$ plane. Two FSRQs and four BL Lacs yielded $H>0.5$, indicating presence of long-term memory in the underlying process governing the variability. Additionally, two FSRQs with exceptional PSDs, stand out also in the $mathcal{A}-mathcal{T}$ plane.
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