How to determine a functor (natrually arising from geometry or homological algebra) to be locally of finite presentation? Is there any reference for such staff?

My example of functors underlying this question is functors of the form $$\mathcal{E}xt^1_S(A,\mathbb{G}_m)$$ for $A$ some group scheme or even some fppf-sheaf of geometric meaning over some base scheme $S$, and $\mathcal{E}xt^1_S(,)$ denotes the 1st fppf extension sheaf in the category of abelian fppf-sheaves over $S$.