Why is the thione tautomeric form of 2-Mercaptopyridine favoured?
Assumption (1) doesn't hold too much precedence in this case, just like in the case of 2-pyridone, so it is a minor thing to consider. In the case of the assumption (2), electronegativity is only a part of it. Sulfur atom can stabilize the negative charge better than oxygen due to it's size. For the same reason, $\ce{CH3SH}$ is a stronger acid than $\ce{CH3OH}$: $\ce{CH3S-}$ is a more stable conjugate base than $\ce{CH3O-}$. So, although sulfur has a lower electronegativity than oxygen, it is still preferred to have a negative charge on it. Thus, altogether, the thione form is more stable than the thiol.

BTW, thank you for a very detailed question and thorough explanation of your reasoning!