The transverse electromagnetic form factors squared of the $^{12}\mathrm{C}$ ${2}^{+}$ levels at 4.439 MeV ($T=0$) and at 16.107 MeV ($T=1$) have been measured by means of 180\ifmmode^\circ\else\textdegree\fi{} electron scattering over a momentum-transfer range from $q=0.51 \mathrm{to} 2.05$ ${\mathrm{fm}}^{\ensuremath{-}1}$. Evidence is presented for appreciable contributions of nuclear convection currents to the transverse 4.439-MeV form factor at low $q$, and spin magnetization contributions to the transverse 16.107-MeV form factor at higher $q$.