To model unsteady airfoil aerodynamics in forward and reverse flows in a simple and robust manner requires a strong understanding of the complex flow dynamics and their relation to first-order concepts. The current work explores the relation between the leading-edge suction force, represented nondimensionally by the leading-edge suction parameter (LESP), and the flow physics of forward and reverse dynamic stall as a function of freestream Reynolds number, airfoil thickness, and motion kinematics for the NACA 0012, 0015, and 0018 airfoils using computational tools. The relation between the LESP and critical events associated with leading-edge vortex (LEV) shedding was found to be independent of flow direction barring the signature to identify LEV initiation. Leading-edge suction was observed to continue to increase after LEV initiation in reverse flow and could be attributed to the combined effect of a weak LEV and strong trailing-edge vortice. While LESP, forces, and moments were found to be moderately dependent on airfoil thickness and strongly dependent on the Reynolds number in forward flow conditions and the critical LESP, in addition, was weakly dependent on motion kinematics, the aerodynamics were observed to be largely independent of said parameters in reverse flow. This allows for a single critical LESP value to be used for symmetric airfoils to indicate LEV initiation when the blunt edge is experiencing reversed flow, a finding which serves to largely reduce the empirical dependencies while modeling unsteady reverse dynamic stall in low-order methods.