Need to get the multimeter out and see what the volatge is whilst running.
The red light just indicates that the battery isn’t receiving sufficient charge, and that can be down to many things.
Alternator shagged
Battery shagged
Wires to battery broken
Aux belt slipping
Bad earth stopping charge
If the alternator has a 12v exciter feed that might not be working.
Blown fuses can be an issue too.
Many many causes indeed
However all are easy to diagnose and rule and and generally cheap to fix unless it’s the battery or alternator, then it’s a little more expensive