  Photometric variability attributed to cloud phenomena is common in L/T transition brown dwarfs. Recent studies show that such variability may also trace aurorae, suggesting that localized magnetic heating may contribute to observed brown dwarf photometric variability. We assess this potential correlation with a survey of 17 photometrically variable brown dwarfs using the Karl G. Jansky Very Large Array (VLA) at 4 -- 8 GHz. We detect quiescent and highly circularly polarized flaring emission from one source, 2MASS J17502484-0016151, which we attribute to auroral electron cyclotron maser emission. The detected auroral emission extends throughout the frequency band at $\sim$5 -- 25$\sigma$, and we do not detect evidence of a cutoff. Our detection confirms that 2MASS J17502484-0016151 hosts a magnetic field strength of $\geq$2.9 kG, similar to those of other radio-bright ultracool dwarfs. We show that H$\alpha$ emission continues to be an accurate tracer of auroral activity in brown dwarfs. Supplementing our study with data from the literature, we calculate the occurrence rates of quiescent emission in L dwarfs with low- and high-amplitude variability and conclude that high amplitude O/IR variability does not trace radio magnetic activity in L dwarfs. 
On the Correlation between L Dwarf Optical and Infrared Variability and   Radio Aurorae