In the mHz gravitational-wave band, galactic ultra-compact binaries (UCBs) are continuous sources emitting at near-constant frequency. The signals from many of these galactic binaries will be sufficiently strong to be detectable by the emph{Laser Interferometer Space Antenna} (LISA) after ${sim}mathcal{O}(1 text{week})$ of observing. In addition to their astrophysical value, these UCBs can be used to monitor the data quality of the observatory. This paper demonstrates the capabilities of galactic UCBs to be used as calibration sources for LISA by demanding signal coherence between adjacent week-long data segments separated by a gap in time of emph{a priori} unknown duration. A parameter for the gap duration is added to the UCB waveform model and used in a Markov-chain Monte Carlo algorithm simultaneously fitting for the astrophysical source parameters. Results from measurements of several UCBs are combined to produce a joint posterior on the gap duration. The measurement accuracys dependence on how much is known about the UCBs through prior observing, and seasonal variations due to the LISA orbital motion, is quantified. The duration of data gaps in a two-week segment of data can be constrained to within stmo using {$mathcal{O}(10)$} UCBs after one month of observing. The timing accuracy from UCBs improves to styr after 1 year of mission operations. These results are robust to within a factor of ${sim}2$ when taking into account seasonal variations.
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