Auroral emissions are an important diagnostic for a planet’s magnetosphere and upper atmosphere. At the outer planets, the characteristics of emission from the triatomic hydrogen ion \({{\rm{H}}}_{3}^{+}\) are key to understanding the auroral energy budget. We present James Webb Space Telescope observations of Jupiter’s infrared auroral \({{\rm{H}}}_{3}^{+}\) emission, exhibiting variability on timescales down to seconds. Together with simultaneous Hubble Space Telescope ultraviolet observations, these results imply an auroral \({{\rm{H}}}_{3}^{+}\) lifetime of 150 s, and that \({{\rm{H}}}_{3}^{+}\) cannot efficiently radiate heat deposited by bursty auroral precipitation. However, \({{\rm{H}}}_{3}^{+}\) radiation is particularly efficient in a dusk active region, which has no significant ultraviolet counterpart. The cause of such emission is unclear. We also present observations of rapid eastward-travelling auroral pulses in the dawn side auroral region and pulsations that propagate rapidly along the Io footprint tail. Together, these observations open a diagnostic window for the jovian magnetosphere and ionosphere.