The near-IR line of Mn I at 15262.7 Å has recently been proposed as a new tool for diagnosing the magnetic field strength and magnetic energy density associated with unresolved magnetic structures, due to the enhanced sensitivity of the Stokes I profile. In this paper, the behavior of the line, focusing on the properties of the Stokes I profile, is analyzed in detail with the aid of state-of-the-art magneto-hydrodynamical simulations of the solar surface convection. The line is synthesized taking into account that the splitting and the strength of the Zeeman components have to be calculated under the framework of the Paschen-Back theory via the numerical diagonalization of the total Hamiltonian, including the hyperfine and Zeeman contributions. The peak ratio and separation of the blue and red lobes of the emergent Stokes I profile are shown to be correlated with the magnetic field strength when no smearing is taken into account, while the correlation slightly degrades when diffraction and stray-light contamination is accounted for. We also analyze the dependence of the first two line moments with the magnetic field, showing that the first and second moments can be used to trace the velocity and the magnetic field strength, respectively. This correlation is still maintained for ground-based observations.