... where the vast majority of that something's mass and charge are within the event horizon. To keep Birkhoff happy, and to avoid confusion with event horizons that pop up where a black hole clearly isn't, maybe add that in a small region of spacetime mass and charge inside an event horizon is a black hole if after stationarization electromagnetic and gravitational perturbations in the Schwarzschild metric are small compared to those in e.g. the Minkowski or Robertson-Walker metrics.

I'm tempted to go the other direction: a physically reasonable arrangement of stress-energy can source a black-hole-like metric and that a black hole metric (i.e., an exact solution for a mathematical black hole, like Kerr-Newman) can usefully approximate such that there is a good match between the geodesics structure around a mathematical black hole and the behaviour of observed matter in the vicinity of a black hole candidate.

A practical probe of the null geodesics structure around a BH candidate is surface emissions: we routinely detect them directly and through analyses of radiative efficiency for neutron stars and white dwarfs (whether or not these compact objects are accreting), and a detection of surface emission from a compact BH candidate would rule it out as a source of a BH metric. If all BH candidates have surface emissions, then BH metrics are a poor choice of modelling tool. However candidates which survive this probe and other tests of near-horizon geodesics structure might as well be called black holes, even if we have reasons to hope (or even doubt) that its mass and charge within the apparent horizon is concentrated in the singularity point.

You'll note here that I'm taking a "quacks like a duck" view of astrophysical black holes; I'd go even further and want to be agnostic about event horizon vs trapping surface and so forth. Around BH-like objects, arranged by increasing ease of observation, there will be a predictable (set of) ISCO(s) below which free-falling trajectories always decay or plunge inward (or outward if retrograde); there will be very strong gravitational lensing; there will be characteristic outflows from Penrose-like mechanisms; and a characteristic efficiency in conversion of accretion matter into radiation compared to matter accreting onto non-BH objects of similar mass. These all depend on whether the exterior region near the candidate object is like that of an exact BH solution, and when you have all of the above, and no evidence to the contrary, it is pretty safe to assume there is something very similar to an event horizon dividing the near-exterior region from the non-exterior region(s).