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The flow under an Eyring-Powell description has attracted interest to model different scenarios related with non-Newtonian fluids. The goal of the present study is to provide analysis of solutions to a one-dimensional Eyring-Powell fluid in Magnetohydrodynamics (MHD) with general initial conditions. Firstly, regularity and bounds of solutions are shown as a baseline to support the construction of existence and uniqueness results. The existence analysis is based on the definition of a Hamiltonian that constitutes the underlying theory to obtain stationary profiles of solutions that are validated with a numerical approach. Afterwards, non-stationary profiles of solutions are explored based on an asymptotic approximation to a Hamilton-Jacobi type of equation. To this end, an exponential scaling is considered together with perturbation methods. Finally, a region of validity for such exponential scaling is provided.