  We demonstrate that Michelson-Morley tests, which detect direction-dependent
anisotropies in the speed of light, can also be used to place limits upon
isotropic deviations of the vacuum speed of light from $c$, as described by the
photon sector Standard Model Extension (SME) parameter $\tilde{\kappa}_{tr}$. A
shift in the speed of light that is isotropic in one inertial frame implies
anisotropic shifts in others. Using observer Lorentz covariance, we derive the
time-dependent variations in the relative resonance frequencies of a pair of
electromagnetic resonators that would be generated by such a shift in the rest
frame of the Sun. A new analysis of a recent experimental test of relativity
using this result constrains $\tilde{\kappa}_{tr}$ with a precision of
$7.4\times10^{-9}$. This represents the first constraint on
$\tilde{\kappa}_{tr}$ by a Michelson-Morley experiment and the first analysis
of a single experiment to simultaneously set limits on all nine
non-birefringent terms in the photon sector of the SME.
