  Let $\phi$ be a Drinfeld $A$-module of finite residual characteristic
$\bar{\mathfrak{p}}$ over a local field $K$. We study the action of the inertia
group of $K$ on a modified adelic Tate module
$\smash{T^\circ_{\text{ad}}}(\phi)$ which differs from the usual adelic Tate
module only at the $\bar{\mathfrak{p}}$-primary component. After replacing $K$
by a finite extension we can assume that $\phi$ is the analytic quotient of a
Drinfeld module $\psi$ of good reduction by a lattice $M\subset K$. The image
of inertia acting on $T^\circ_{\text{ad}}(\phi)$ is then naturally a subgroup
of $\operatorname{Hom}_A(M,T^\circ_\text{ad}(\psi))$.
  This subgroup is described by a canonical local Kummer pairing that we study
extensively in this article. In particular we give an effective formula for the
image of inertia up to finite index, and obtain a necessary and sufficient
condition for this image to be open. We also determine the image of the
ramification filtration
