Variability is examined in over 2.6 million stars covering 11 square degrees of the core of the Sagittarius dwarf spheroidal galaxy (Sgr dSph) from Visible and Infrared Survey Telescope for Astronomy Z-band observations. Generally, pulsation on the Sgr dSph giant branches appears to be excited by the internal kappa mechanism. Pulsation amplitudes appear identical between red and asymptotic (red giant branch/asymptotic giant branch) giant stars, and between unreddened carbon and oxygen-rich stars at the same luminosity. The lack of correlation between infrared excess and variability among oxygen-rich stars indicates that pulsations do not contribute significantly to wind driving in oxygen-rich stars in the Sgr dSph, though the low amplitudes of these stars mean this may not apply elsewhere. The dust-enshrouded carbon stars have the highest amplitudes of the stars we observe. Only in these stars does an external kappa-mechanism-driven pulsation seem likely, caused by variations in their more opaque carbon-rich molecules or dust. This may allow pulsation driving of winds to be effective in carbon stars. Variability can be simplified to a power law (A proportional to L/T-2), as in other systems. In total, we identify 3026 variable stars (with rms variability of delta Z greater than or similar to 0.015 mag), of which 176 are long-period variables associable with the upper giant branches of the Sgr dSph. We also identify 324 candidate RR Lyrae variables in the Sgr dSph and 340 in the outer Galactic bulge.