We present results of X-ray spectral and time-domain variability analyses of 4 faint, "quiescent" blazars from the Swift-BAT 105-month catalog. We use observations from a recent, 5-month long NICER campaign, as well as archival BAT data. Variations in the 0.3-2 keV flux are detected on minute, ∼weekly, and monthly timescales, but we find that the fractional variability 𝐹 var on these timescales is <25% and decreases on longer timescales, implying generally low-amplitude variability across all sources and showing very low variability on monthly timescales (𝐹 var 13%), which is at odds with previous studies that show that blazars are highly variable in the X-rays on a wide range of timescales. Moreover, we find that the flux variability on very short timescales appears to be characterized by long periods of relative quiescence accompanied by occasional short bursts, against the relatively time-stationary nature of the variability of most other AGN light curves. Our analysis also shows that the broadband X-ray spectra (0.3-195 keV) of our sources can be described with different power law models. As is the case with most blazars, we find that 2 sources (2MASS J09343014-1721215 and PKS 0312-770) are well-modeled with a simple power law, while the remaining two (1RXS J225146.9-320614 and PKS 2126-15) exhibit curvature in the form of a log-parabolic power law. We also find that, in addition to the continuum, PKS 2126-15 requires significant absorption at the soft X-rays ( 1 keV) to fully describe the observed curvature, possibly due to absorption from the intergalactic medium.