Magnetic fields are fundamental in regulating star formation and the evolution of molecular clouds. Zeeman splitting offers a unique method to directly measure line-of-sight magnetic field strengths in interstellar environments, from the diffuse ISM to dense cores. Observations of HI and OH absorption toward pulsars provide an unprecedented opportunity to measure magnetic fields with high precision, benefiting from pulsars' small angular sizes and reliable Stokes V spectra unaffected by instrumental effects. Our recent tentative Zeeman splitting detections in OH absorption toward PSR J1644-4559 with Parkes reveal magnetic field strengths that suggest magnetically subcritical states, where magnetic pressure counteracts gravity. This challenges conventional theories of subcritical cold neutral medium (CNM) transitioning to supercritical star-forming molecular clouds, emphasizing the need for detailed investigation. We propose a continuation of Zeeman splitting studies through high-sensitivity OH and HI absorption observations of pulsars PSR J1644-4559, J1721-3532, and J1852+0031 using Parkes. By employing an innovative phase-resolved spectral technique and extending integration times, we aim to enhance Zeeman detection sensitivity and study magnetic field transitions in the CNM and quiescent molecular clouds. This work will refine our understanding of subcritical-to-supercritical transitions in star formation, establish pulsar absorption as a robust probe of interstellar magnetic fields, and advance observational techniques critical to star formation studies.