Debris discs which orbit white dwarfs are signatures of remnant planetary systems. We present 12 yr of optical spectroscopy of the metal-polluted white dwarf SDSS J1228+1040, which shows a steady variation in the morphology of the 8600 A Ca II triplet line profiles from the gaseous component of its debris disc. We identify additional emission lines of O-I, Mg-I, Mg-II, Fe II and Ca II in the deep co-added spectra. These emission features (including Ca H & K) exhibit a wide range in strength and morphology with respect to each other and to the Ca II triplet, indicating different intensity distributions of these ionic species within the disc. Using Doppler tomography, we show that the evolution of the Ca II triplet profile can be interpreted as the precession of a fixed emission pattern with a period in the range 24-30 yr. The Ca II line profiles vary on time-scales that are broadly consistent with general relativistic precession of the debris disc.