2005 Mazda 6 2.3l battery light/alternator issue

First time poster long time lurker. I have a 2005 Mazda 6 I sport with a 2.3l 4 cyl. Right around 140,000 miles. Recently had battery light come on and had the alternator replaced. Car ran good for a week and now the battery light is back on and it’s shifting into limp mode again. Took it back to shop and they couldn’t duplicate the light and checked the wiring etc Incase something was loose. Picked it up and within 5 minutes I duplicated the battery light. Seemed to do it in 3rd gear when I clear 3000 rpm and in 4th gear when I clear 3400 rpm. When hooked up to voltage tester everything checks out fine.

Not sure what the next step is. I didn’t really want to go to a dealership for a 15 year old car and put a ton more money into this car. It’s been a good car for the 12 years I’ve owned it until this issue.

Any help or guidance is greatly appreciated.
 

rsvinylgraphics

2008.5 MGM MS3
Contributor
:
2008.5 MS3
In my 2008 MX5, the battery light also can indicate low brake fluid level. As the pads wear, more fluid is pulled from the reservoir, eventually leading to a brake light that will illuminate when the sensor "sees" the low fluid condition because of the tilt of the car.
After I picked up my MX5, I noticed this happening every so often. When I popped open the reservoir cap, it was obvious that the level was low. I filled it and never saw the light again. Note that whenever the pads are replaced, you should have the fluid flushed.

Two things, low brake fluid will trigger the "brake" warning light not the battery light.
Changing only the pads does not require opening the system, therefore no need to do a brake system flush.
 
:
2014 Mazda3 S GT auto, 2008 MX5 6-speed
Okay, back to the real (vs brake) question and suggestion:
Did you have a load test done to your battery? Doing a simple voltage test is not the best way to test a battery. Even if the battery is less than 3 years old, it could be weak.