  The operation of the next generation of gamma-ray observatories will lead to
a great advance in dark matter searches. In this paper, we use the hidden
sectors hypothesis within the so-called secluded models to calculate the
capabilities of the Southern Wide-field Gamma-ray Observatory (SWGO) to detect
gamma-ray signatures produced by dark matter particles concentrated in the Sun.
We assume the dark matter particle annihilates into metastable mediators which
decay into $\gamma\gamma$, $e^+e^-$, $\tau^+\tau^-$, and $\bar{b}b$ outside the
Sun. We found that the SWGO will be able to probe a spin-dependent
cross-section of about $10^{-46}$ cm$^2$ for dark matter masses smaller than 5
TeV. This result shows an unprecedented sensitivity surpassing the current
instruments by more than one order of magnitude.
