  We introduce a new approach to investigate the selection rules governing the
contributions of fluxed M5-instantons to the F-theory four-dimensional
effective action, with emphasis on the generation of charged matter F-terms.
The structure of such couplings is unraveled by exploiting the perturbative and
non-perturbative homological relations, introduced in our companion paper
arXiv:1506.06764, which encode the interplay between the self-dual 3-form flux
on the M5-brane, the background 4-form flux and certain fibral curves. The
latter are wrapped by time-like M2-branes representing matter insertions in the
instanton path integral. In particular, we clarify how fluxed M5-instantons
detect the presence of geometrically massive $U(1)$s which are responsible for
`hidden' selection rules. We discuss how for non-generic embeddings the
M5-instanton can probe `locally massless' $U(1)$ symmetries if the rank of its
Mordell-Weil group is enhanced compared to that of the bulk. As a
phenomenological off-spring we propose a new type of non-perturbative
corrections to Yukawa couplings which may change the rank of the Yukawa matrix.
Along the way, we also gain new insights into the structure of massive $U(1)$
gauge fluxes in the stable degeneration limit.
