  We revisit the characterisation of modules over non-unital $C^*$-algebras
analogous to modules of sections of vector bundles. A fullness condition on the
associated multiplier module characterises a class of modules which closely
mirror the commutative case. We also investigate the multiplier-module
construction in the context of bi-Hilbertian bimodules, particularly those of
finite numerical index and finite Watatani index.
