Hyperpolarization of 13C-pyruvate via Signal Amplificaton By Reversibble Exchange (SABRE) is an important recent discovery because of both the relative simplicity of hyperpolarization and the central biological relevance of pyruvate as a biomolecular probe for in vitro or in vivo studies. Here, we analyze the [1,2-13C2]pyruvate-SABRE spin system and its field dependence theoretically and experimentally. We provide first-principles analysis of the governing 4-spin dihydride-13C2 Hamiltonian and numerical spin dynamics simulations of the 7-spin dihydride-13C2-CH3 system. The analytical and the numerical results are compared to matching systematic experiments. With these methods we unravel the observed spin state mixing of singlet states and triplet states at microTesla fields and we also analyze the dynamics during transfer from micro-Tesla field to high field for detection to understand the resulting spectra from the [1,2-13C2]pyruvate-SABRE system.