When you turn the ignition key to the on position before starting, do you get all your dash indicator lights including the battery or no. Does it come on after you start driving?
Was it working before? If you plug a scanner in to look at your system, are you getting any codes? Does any code need to be reset after you changed the alternator? How much voltage do you see on the battery using a tester, and after you remove the surface charge?
The dash battery lamp indicator is normally off but yes, it fires up briefly when you turn your key to the ignition pre-start position and goes out after the engine starts. Of course, if it comes on when your engine is running, it may be telling you about a low charge condition, wiring problems or alternator problems.
Rather than crawling around under the dash at this point, which is towards the end of the circuit, I’d start at the front and work backwards by first systematically checking your battery voltage and testing to ensure your alternator is really charging the battery when the engine is running. If you see a problem on your meter, check the connections for the alternator and your battery clamps and any assoc. wiring there. A parts store could help you check for codes, a repair shop could test your alternator and charging system.
If the system electrical tests ok, then that would tell me you’re chasing an electrical open in the dash light system. Check for any other dash lights being off, fuses, etc., then test for power at the wiring connector(s) that feed the dash indicator lamps working your way up to the socket itself which is likely hard to get to unless you’re a contortionist.
IMO, if the lamp was lighting before you started this operation, it ain’t likely it’s the lamp. Look at a wiring diagram to see if the battery lamp shares it’s juice source with other lamps on the dash or common fuses.
Mark