This paper develops a vortex-based model of the photon as an alternative mechanical picture of quantum electrodynamics (QED), grounded in the Kelvin-Voigt (K-V) viscoelastic analogy for Maxwell's equations established in a companion work. In that framework, a dilute assembly of compact vortex rings in an incompressible viscoelastic medium obeys equations formally identical to Maxwell's equations, with the electromagnetic vector potential identified as proportional to the solenoidal velocity field of the medium. Within this model a photon is represented as a propagating vortex ring whose orientation is parameterized by two angles. It is shown that the transverse far-field components of the vortex trajectory map exactly onto the Jones formalism for polarization, recovering the full Poincare sphere of polarization states. The propagating mode is strictly transverse, as required by QED, because the incompressibility of the K-V medium enforces the Coulomb gauge identically. The model's distinctive prediction concerns the near-field region: for a non-circularly polarized photon, a non-zero longitudinal mechanical displacement of the vacuum medium exists at sub-wavelength distances from the photon path. This evanescent near-field component does not propagate as a wave and is absent from standard QED, which predicts no sub-wavelength near-field structure for free photons in vacuum. Two falsifiable experimental tests are proposed. The first uses photon-induced near-field electron microscopy (PINEM) to search for a polarization-dependent longitudinal field component at transverse distances of 80-250 nm from a laser beam in open vacuum. The second probes the angular momentum balance during single-photon absorption in a laser-cooled trapped ion, looking for an excess orbital recoil tied to the vortex circulation invariant. Standard QED predicts strictly negative results in both experiments; any confirmed positive signal would constitute evidence for the mechanical structure of the vacuum medium.