  In this paper we prove existence for model knot solutions to the
dimensionally reduced twisted Kapustin-Witten equations on $\mathbb{R}^3_+$ for
any twisting parameter $t\in(0,\infty)$. We start with the explicit solutions
for $t = 1$ derived in \cite{WFivebranes} and perform a continuity argument in
$t$. This corroborates a prediction of Gaiotto and Witten \cite[][p. 961]{GW}.
