Fuzzy dark matter (FDM) has dynamical properties that differ significantly from cold dark matter (CDM). These dynamical differences are strongly manifested on the spatial scale of dwarf spheroidal galaxies (dSphs), which roughly corresponds to the de Broglie wavelength of a canonical mass FDM particle. We study simulations of a dSph satellite which is tidally perturbed by its host galaxy, in order to identify dynamical signatures that are unique to FDM, and to quantify the imprints of such perturbations on an observable stellar tracer population. We find that a perturbed FDM soliton develops a long-standing breathing mode, whereas for CDM such a breathing mode quickly phase-mixes and disappears. We also demonstrate that such signatures become imprinted on the dynamics of a stellar tracer population, making them observable with sufficiently precise astrometric measurements.