  We propose a general model where quintessence couples to electromagnetism via
its kinetic term. This novelty generalizes the linear dependence of the gauge
kinetic function on $\phi$, commonly adopted in the literature. The interaction
naturally induces a time variation of the fine-structure constant that can be
formulated within a disformally coupled framework, akin to a Gordon metric.
Through a suitable parametrization of the scalar field and the coupling
function, we test the model against observations sensitive to the variation of
$\alpha$. We undertake a Bayesian analysis to infer the free parameters with
data from Earth based, astrophysical and early Universe experiments. We find
that the evolution of $\alpha$ is specific to each cosmological era and slows
down at late times when dark energy accelerates the Universe. While the most
stringent bound on the interaction is obtained from atomic clocks measurements,
the quasars provide a constraint consistent with weak equivalence principle
tests. This promising model is to be further tested with upcoming and more
precise astrophysical measurements, such as those of the ESPRESSO spectrograph.
