No dash battery, coolant level lights when starting??

[AWDPetmitsu]

My dash battery and coolant level lights don't light up when I turn the key to the ON position, engine off. The headlights and all interior lights were dim when it was running earlier. It wouldn't start like the battery is dead but it'll start if you let it sit for awhile. Then it'll sputter and die after a couple of minutes running.

The alternator and battery were just replaced 2 months ago. I know either can be defective even when replaced. The 80 amp alternator fuse looks good. I've yet to check the fusible link from the alternator to the starter and haven't checked battery voltage nor charging voltage (meter is at workplace.)

What am I missing? Mainly, why aren't my battery and coolant level lights lighting up with the key in the ON position, with the engine off?
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[AWDPetmitsu]

OK-update. 80 amp fuse is definitely good. It would not start this morning. I charged up my old battery, installed it and started it up. I measured across the battery terminals with it running and got 12 volts. I measured voltage at the B terminal on the alternator to chassis ground and got 12 volts. I revved it and voltage at the B terminal went down to 11.99 volts. Shouldn't I be getting 14 volts at the B terminal?

By the way, the replacement alternator is a genuine remanufactured Mitsubishi unit. I just installed it 2 months ago but I know it could be defective.

If it's not charging, why isn't my battery light coming on? I doubt it's the bulb because the coolant level light isn't on either.

My conclusion is that the alternator is defective and that the 12 volts I'm getting at the B terminal is actually the battery voltage being measured. So this means that the circuit to charge the battery from the alternator to the battery is good. Is this all correct?

 

[Defiant]

I'm with the bad alternator diagnosis.
I wonder what the numbers are for bum rebuilts across the industry. I swear it has to run an easy 25%. It must cost them nothing to "rebuild" an alternator, going by how many they have to re-rebuild.

 

[AWDPetmitsu]

Just updating. It was a faulty alternator. I replaced it with another remanufactured factory unit and the battery and coolant lights illuminate with the key on, engine off. Ironic that I went with OEM instead of aftermarket just to avoid this, but it still failed.