  In this paper, we study p-adic endoscopy on eigenvarieties for
$\mathrm{SL}_2$ over totally real fields, taking a geometric perspective. We
show that non-automorphic members of endoscopic L-packets of regular weight
contribute eigenvectors to overconvergent cohomology at critically refined
endoscopic points on the eigenvariety, and we precisely quantify this
contribution. This gives a new perspective on and generalizes previous work of
the second author. Our methods are geometric, and are based on showing that the
$\mathrm{SL}_2$-eigenvariety is locally a quotient of an eigenvariety for
$\mathrm{GL}_2$, which allows us to explicitly describe the local geometry of
the $\mathrm{SL}_2$-eigenvariety. In particular, we show that it often fails to
be Gorenstein at such points.
