Spiral arms have been observed in more than a dozen protoplanetary disks, yet the origin of nearly all systems is under debate. Multi-epoch monitoring of spiral arm morphology offers a dynamical way in distinguishing two leading arm formation mechanisms: companion-driven, and gravitational instability induction, since these mechanisms predict distinct motion patterns. By analyzing multi-epoch J-band observations of the SAO 206462 system using the SPHERE instrument on the Very Large Telescope (VLT) in 2015 and 2016, we measure the pattern motion for its two prominent spiral arms in polarized light. On one hand, if both arms are comoving, they can be driven by a planet at $86_{-13}^{+18}$ au on a circular orbit, with gravitational instability motion ruled out. On the other hand, they can be driven by two planets at $120_{-30}^{+30}$ au and $49_{-5}^{+6}$ au, offering a tentative evidence (3.0$sigma$) that the two spirals are moving independently. The independent arm motion is possibly supported by our analysis of a re-reduction of archival observations using the NICMOS instrument onboard the Hubble Space Telescope (HST) in 1998 and 2005, yet artifacts including shadows can manifest spurious arm motion in HST observations. We expect future re-observations to better constrain the motion mechanism for the SAO 206462 spiral arms.