Odds of battery just dying?

I've never come across a problem like this, so I figured I'd throw it out there.

I have a 1967 273 Barracuda, and is pretty original.
No extra accessories or hack jobs.
No air, just motor and typical items, lights, AM radio.

After nipping a slight power steering leak I figured I would get a little more drive time in.
I drive to work, no issues. Drive home afterwards, no issues.
Get home and Mother in Law is over and blocking drive, so I park behind her.
She goes to leave and I hit the key and it clicks as if the solenoid is going to engage and then nothing.
And then I realize even the dome light is out.

I still had the original Amp meter and was functioning but honestly on drive home paid zero attention to it.

So I get my multimeter out the next day and do a little searching.
12.7 at battery. I know this is NOT the full story of a healthy battery.
12 plus volts all the way through bulkhead and was pleasantly surprised to see a PO has done a VERY good bulkhead terminal elimination for the "hot" in and alt through as well.
Now I notice dome light is on.
I turn head lights on and it goes off.
Unhook battery and dome light back on.
Honk horn and it makes a rather croaky noise.
Hit key to start and nothing happens and dome light back off.
I can get very low power things to "come a little alive" but any serious draw shuts everything down.
I pull dash as curious as to the Amp meter and the multi-splice for all power in cabin.
Everything looks great.
No previous hacks, no "heated" or "melted wires" or nothing.
So I measure volts at the splice after Amp meter.
As I turn on accessories I see the volts drop, like a lot.
Dome light goes to around 11, flashers to less than 10 and so on.

So back to my battery, it's an old battery of unknown age.
Heck I've had the car 2 years now alone.

So, can a battery just go like that?
I figured I'll run it up to a parts store and have them test it, but I've had batteries crap out before and never like that.

Thanks for the input.