The atomic interstellar medium shows tiny-scale optical depth fluctuations on the scale of 0.1~10,000 AU, whose origin and nature are poorly understood. The existence of this Tiny-Scale Atomic Structure (TSAS) has significant implications, potentially calling into question our fundamental understanding of heating, cooling and dynamical processes in the interstellar medium. Yet observations remain sparse. This long-term project plans to search for temporal variations in HI absorption spectra seen against background pulsars to characterise TSAS in the Milky Way interstellar medium (ISM). These observations constitute the largest number of sightlines and densest temporal sampling ever performed in a single experiment, and will test predictions that TSAS is the tail end of a turbulent cascade, constrain its minimum size scale (down to resolutions of ~0.05 AU) and potentially provide the first direct measurements of pressures in "large" TSAS features of > 1000 AU. We make use of the phase-resolved spectral line mode that we have recently implemented on Parkes, which has cut data rates and processing times by factors of ~1000 compared to past studies. This is an expansion of our pilot P1321 to a long term study.