A search for a time-varying νe signal was performed with 621 days of data acquired by the Daya Bay Reactor Neutrino Experiment over 704 calendar days. The time spectrum of the measured νe flux normalized to its prediction was analyzed with a Lomb-Scargle periodogram, which yielded no significant signal for periods ranging from 2 hours to nearly 2 years. The normalized time spectrum was also fit for a sidereal modulation under the Standard Model Extension (SME) framework to search for Lorentz and CPT violation (LV-CPTV). Limits were obtained for all six flavor pairs ēμ,ēτ, μτ, ēē,μμ and ττ by fitting them one at a time, constituting the first experimental constraints on the latter three. Daya Bay's high statistics and unique layout of multiple directions from three pairs of reactors to three experimental halls allowed the simultaneous constraint of individual SME LV-CPTV coefficients without assuming others contribute negligibly, a first for a neutrino experiment.