We present a study of 323 photometrically variable young stellar objects that are likely members of the North America and Pelican nebulae star-forming region. To do so, we utilize over two years of data in the g and r photometric bands from the Zwicky Transient Facility. We first investigate periodic variability, finding 46 objects (~15% of the sample) with significant periods that phase well and can be attributed to stellar rotation. We then use the quasiperiodicity (Q) and flux asymmetry (M) variability metrics to assign morphological classifications to the remaining aperiodic light curves. Another ~39% of the variable star sample beyond the periodic (low Q) sources are also flux-symmetric, but with a quasiperiodic (moderate Q) or stochastic (high Q) nature. Concerning flux-asymmetric sources, our analysis reveals ~14% bursters (high negative M) and ~29% dippers (high positive M). We also investigate the relationship between variability slopes in the g versus g-r color-magnitude diagram, and the light-curve morphological classes. Burster-type objects have shallow slopes, while dipper-type variables tend to have higher slopes that are consistent with extinction-driven variability. Our work is one of the earliest applications of the Q and M metrics to ground-based data. We therefore contrast the Q values of high-cadence and high-precision space-based data, for which these metrics were designed, with Q determinations resulting from degraded space-based light curves that have the cadence and photometric precision characteristic of ground-based data.