The emission of white light from a single material is atypical and is of interest for solid-state lighting applications. Broadband light emission has been observed in some layered perovskite derivatives, A2PbBr4 (A = R-NH3+), and correlates with static structural distortions corresponding to out-of-plane tilting of the lead bromide octahedra. While materials with different organic cations can yield distinct out-of-plane tilts, the underlying origin of the octahedral tilting remains poorly understood. Using high energy resolution (e.g., quasi-elastic) neutron scattering, this contribution details the rotational dynamics of the organic cations in A2PbBr4 materials where A = n-butylammonium (nBA), 1,8-diaminooctammonium (ODA), and 4-aminobutyric acid (GABA). The organic cation dynamics differentiate (nBA)2PbBr4 from (ODA)PbBr4 or (GABA)2PbBr4 in that the larger spatial extent of dynamics of nBA yields a larger effective cation radius. The larger effective volume of the nBA cation in (nBA)2PbBr4 yields a closer to ideal A-site geometry, preventing the out-of-plane tilt and broadband luminescence. In all three compounds, we observe hydrogen dynamics attributed to rotation of the ammonium headgroup and at a time scale faster than the white light photoluminescence studied by time-correlated single photon counting spectroscopy. This supports a previous assignment of the broadband emission as resulting from a single ensemble, such that the emissive excited state experiences many local structures faster than the emissive decay. The findings presented here highlight the role of the organic cation and its dynamics in hybrid organic–inorganic perovskites and white light emission.