In this third paper in a series presenting observations by the Cassini Ultraviolet Imaging Spectrometer (UVIS) of the Io plasma torus, we show remarkable, though subtle, spatio-temporal variations in torus properties. The Io torus is found to exhibit significant, near-sinusoidal variations in ion composition as a function of azimuthal position. The azimuthal variation in composition is such that the mixing ratio of S II is strongly correlated with the mixing ratio of S III and the equatorial electron density and strongly anti-correlated with the mixing ratios of both S IV and O II and the equatorial electron temperature. Surprisingly, the azimuthal variation in ion composition is observed to have a period of 10.07 hours-1.5% longer than the System III rotation period of Jupiter, yet 1.3% shorter than the System IV period defined by Brown (1995). Although the amplitude of the azimuthal variation of S III and O II remained in the range of 2-5%, the amplitude of the S II and S IV compositional variation ranged between 5-25% during the UVIS observations. Furthermore, the amplitude of the azimuthal variations of S II and S IV appears to be modulated by its location in System III longitude, such that when the region of maximum S II mixing ratio (minimum S IV mixing ratio) is aligned with a System III longitude of ∼200±15 • , the amplitude is a factor of ∼4 greater than when the variation is anti-aligned. This behavior can explain numerous, often apparently contradictory, observations of variations in the properties of the Io plasma torus with the System III and System IV coordinate systems.