The Battery Light and ABS Light in the cluster are like most of the other warning lights, they each get 12volts with Key ON, and are then Grounded by their respective devices/units which causes them to light up
The Battery Light circuit does have a resistor by-pass in case bulb should burn out, so alternator doesn't quit working
But shouldn't matter if bulb is LED or incandescent.
Simple test would be to test battery voltage engine off, 12.3v to 12.8volt is expected
Then start engine and re-test battery voltage, 14.3v to 14.8volt is expected<<<if still 12volt then alternator is OFF, not working
ABS bulb doesn't have a by-pass its just gets 12v key on and ABS module grounds it to light it up
Both of these bulbs ground wires are on the 10 pin connector on the cluster, may be they got shorted to ground when plugging back in cluster
If alternator is not working then unplug the 3 wire connector on alternator, test light green wire, it should have 12v with key on/engine off
If not then LED is blocking voltage so you would have to change it back to incandescent bulb
LED stands for "light emitting DIODE" and a diode only allows electricity to flow ONE-WAY, which can be a problem in a circuit like that