The Event Horizon Telescope (EHT) has unveiled the horizon-scale radiation properties of Sagittarius A* (Sgr A*), the supermassive black hole at the center of our galaxy, providing a novel platform for testing gravitational theories by comparing observations with theoretical models. A key next step is to investigate the nature of accretion flows and spacetime structures near black holes by analyzing the time variability observed in EHT data alongside general relativistic magnetohydrodynamic (GRMHD) simulations. We explored the dynamics of accretion flows in spherically symmetric black hole spacetimes with deviations from general relativity utilizing two dimensional GRMHD simulations based on the Rezzolla–Zhidenko parameterized spacetime. This study marks the first systematic investigation into how variability amplitudes in light curves, derived from non-Kerr GRMHD simulations, depend on deviations from the Schwarzschild spacetime. The deviation parameters are consistent with the constraints from weak gravitational fields and the size of Sgr A*’s black hole shadow. We find that the dynamics of accretion flows systematically depend on these parameters. In spacetimes with a deeper gravitational potential, fluid and Alfvén velocities consistently decrease relative to the Schwarzschild metric, indicating weaker dynamical behavior. We also examined the influence of spacetime deviations on radiation properties by computing luminosity fluctuations at 230 GHz using general relativistic radiative transfer simulations, in line with EHT observations. The amplitude of these fluctuations exhibits a systematic dependence on the deviation parameters, decreasing for deeper gravitational potentials compared to the Schwarzschild metric. These features are validated using one of the theoretically predicted metrics, the Hayward metric, a model that describes nonsingular black holes. This characteristic is expected to have similar effects in more comprehensive simulations that include more realistic accretion disk models and electron cooling in the future, potentially aiding in distinguishing black hole solutions that explain the variability of Sgr A*.