Is the meter showing 14v at the same time the red battery light is on?
Must be honest, if I were getting 14v across the battery, whilst the car's running, not sure I'd run straight to thinking i had an alternator problem.
However, I think I might take the alternator out, pop the end off and at least clean it thoroughly with some electrical component aerosol spray cleaner. Can only help. Could perhaps be a VR problem in the alternator internal wiring?
could it actually be a battery problem, rather than an alternator problem? How old is the battery? Do you have another battery you could briefly swap in?