RBM wrote:
....

But, it also sounds like the system may not be properly grounded either,
which makes me question how safe the wiring is. ...

Well, we can't tell; I added the caveat first go that presuming OP did
indeed verify this is a continuous connection back to the neutral bus,
not the ground. If that really is the case, it isn't unsafe
electrically, just not Code-compliant on the colors.

It could quite easily be a two-wire circuit in the time frame which are
grandfathered.

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