New alternator, new battery, battery light still on

Hi folks, I have a 2006 Mazda5 with 477,000 km on it :) . At this point it is really just a backup car. After about a year of not driving it I have decided to bring it back to life as a fun project.

Previously it had stalled on me because the alternator was at the end of its life. The battery light went on at that time, i.e. about a year ago. I have just replaced the battery and the alternator but the battery light is still on. I have found this thread, just wondering if anyone has any additional ideas.

When I was removing the old alternator I wasn't very nice to the alternator harness as it was seized and pretty much welded in :). After I replaced the alternator and the battery and noticed the battery light was still on I took some voltage measurements:

1) Engine off: battery: about 12.6 V
2) Engine on, voltage at the alternator terminal: 13.5 V
3) Engine on, voltage arriving at the battery terminals from the alternator: 13.2 V
4) Engine on, battery disconnected while engine running, voltage at the terminals: 13.2 V
5) Engine on, battery disconnected while engine running, all electric things turned on: 13.1 - 13.2 V

So, even without the battery the alternator was able to handle the workload just fine, the engine was still running.

Q1. Do these voltage readings look normal to you? Most websites mention the alternator should produce around 14.6 V, which, if true for Mazda5 as well, could imply the aftermarket alternator is not as good as the OEM one.

Q2. Since the alternator can run the car on its own and there's charging voltage at the battery terminals, it safe to drive the car? I have taken it for two drive tests already, about 1 hour each, the car was running fine.

Q3. Assuming the harness is all right (going to check it next), what else could possibly be wrong? Is there perhaps a single wire that I should check which is responsible for the battery light turning on/off?

Thanks for any ideas.
Update: I should have read the workshop manual which says that generator voltages between 13-15 V are normal. Also:

Generator Warning Light
1. Verify that the battery is fully charged.
2. Verify that the drive belt deflection/tension is correct. (See 01–10A–2 DRIVE BELT INSPECTION [L8, LF].)
3. With the ignition switch turned to the ON position, verify that the generator warning light illuminates.
• If it does not illuminate, inspect the generator warning light and the wiring harness.
— If the generator warning light and the wiring harness are normal, inspect the PCM.
4. Verify that the generator warning light goes off after the engine is started.
• If it does not go out, inspect if any one of the following DTCs in the on-board diagnostic system are
displayed: P0112, P0113, P2502, P2503, P2504. (See 01–02A–9 DTC TABLE [L8, LF].)

Well guess what. I do have P0113 (and also P0102) firing up! Let me dig deeper into this :)
I have to admit I'm laughing at myself now. When I was changing the air filter I forgot to plug the MAT sensor back in :) That was it. No more battery light. Who knew! :)

The long story is that the car had been firing off a check engine code meaning the catalytic convertor was shot, and I had been ignoring that for years. Not worth fixing on such an old car. When I started up the car after a year I was assuming the check engine code was for the cat convertor. It was not! Lesson learned.

In fact, the car is firing no more codes now, not even the old one. Let's see if I can get 500,000 K out of it.
2010 Mazda 5 Sport
A plugged cat can really screw up a car so keep an eye on it. But no codes is no codes.

Idiot lights. They should be against the law. Codes with descriptions would save everyone so much hassle.