What makes eBART light rail?
As far as I can see, eBART is just a standard gauge un-electrified rail line that is fully segregated - not even a level crossing, let alone street-running. That's different to BART's non-standard gauge electrified heavy rail line, but not different to heavy rail.
The trains used are the same as regional Dutch rail.
The American Public Transport Authority classes it, alongside BART, as Commuter Rail. Both also fit the definition of Metro (save, perhaps, the unelectrified nature of eBART).