  Dark matter capture and annihilation in the Sun can produce detectable
high-energy neutrinos, providing a probe of the dark matter-proton scattering
cross section. We consider the case when annihilation proceeds via long-lived
dark mediators, which allows gamma rays to escape the Sun and reduces the
attenuation of neutrinos. For gamma rays, there are exciting new opportunities,
due to detailed measurements of GeV solar gamma rays with Fermi, and
unprecedented sensitivities in the TeV range with HAWC and LHAASO. For
neutrinos, the enhanced flux, particularly at higher energies ($\sim$TeV),
allows a more sensitive dark matter search with IceCube and KM3NeT. We show
that these search channels can be extremely powerful, potentially improving
sensitivity to the dark matter spin-dependent scattering cross section by
several orders of magnitude relative to present searches for high-energy solar
neutrinos, as well as direct detection experiments.
