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"a Chariot is
always treated as a single model"

"Invulnerable saves are different to armour saves because they may always be
taken whenever the model suffers a Wound or, in the case of vehicles, suffers
a penetrating or glancing hit – the Armour Piercing value of attacking
weapons has no effect on an invulnerable save. Even if a Wound, penetrating
hit or glancing hit ignores all armour saves, an invulnerable saving throw can
still be taken."

Armor save also refers to "model." So, does the chariot benefit from a save/invuln save of the Overlord?

Are we talking about a Phase Shifter? Check the rule for the item and it specifically mentions it does not confer to the Chariot.

An armour save is part of the rider's profile, so I think you'll have difficulty convincing people that you can take it on the chariot too. That said, the chariot rules are a bit of a mess on that front, so it's possible that it is meant to be able to use it, but unlikely in my opinion.

I forgot about the Phase Shifter actually saying it's a no-go. So I guess I'm just needing to find something on the armor save. If the PS actually states it's rider only, and there's nothing stating it for an armor save, then I would lean toward it being allowed. But I've only been jamming 40k for about 2 months now :/

The rules for armor saves are clear that you can only make armor saves against wounds suffered.

Vehicles don't suffer wounds

Okay. Got it. Thanks for helping me work through it!