SW Sextantis stars are fundamental to understanding how cataclysmic variables evolve. Their maverick behavior and unexplained accumulation in the orbital period range 3-4 h, about to enter the ``period gap'' where mass transfer is predicted to cease until a period of 2 h is reached, challenge the current evolution theory. To characterize these systems better, we need to determine the nature of the accreting white dwarf and the more normal donor star. But they are usually invisible due to the extreme accretion luminosity these systems normally show. The only chances of characterizing the stars in the system are during rare ``low states'', when the mass transfer rate reaches a minimum for months and the stars are exposed to observations and, therefore, binary parameters measurement. Only dynamical mass measurements can address the evolutionary status. This is a proposal to continue to monitor the brightness of a select group of SW Sextantis stars begun when STScI was a member of the SMARTS consortium to determine their long-term accretion history and, to provide warning when they are entering faint states. The data are essential to characterize the recurrence and duration of these states (likely related to magnetic cycles in the donor star), and trigger our TOO programs in 8-m class telescopes.