The variability of young stellar objects is mostly driven by star-disk interactions. In long-term photometric monitoring of the accreting T Tauri star GI Tau, we detect extinction events with typical depths of Delta V similar to 2.5 mag that last for days to months and often appear to occur stochastically. In 2014-2015, extinctions that repeated with a quasi-period of 21 days over several months are the first empirical evidence of slow warps predicted by magnetohydrodynamic simulations to form at a few stellar radii away from the central star. The reddening is consistent with R-V = 3.85 +/- 0.5 and, along with an absence of diffuse interstellar bands, indicates that some dust processing has occurred in the disk. The 2015-2016 multiband light curve includes variations in spot coverage, extinction, and accretion, each of which results in different traces in color-magnitude diagrams. This light curve is initially dominated by a month-long extinction event and a return to the unocculted brightness. The subsequent light curve then features spot modulation with a 7.03 day period, punctuated by brief, randomly spaced extinction events. The accretion rate measured from U-band photometry ranges from 1.3 x 10(-8) to 1.1 x 10(-10) M-circle dot yr(-1) (excluding the highest and lowest 5% of high- and low- accretion rate outliers), with an average of 4.7 x 10(-9) Me yr(-1). A total of 50% of the mass is accreted during bursts of >12.8 x 10(-9) M-circle dot yr(-1), which indicates limitations on analyses of disk evolution using single-epoch accretion rates.