To check if it is indeed the brushes in the alternator sticking, simply start the engine and presuming the red light is on, tap the rear of the alternator (and the black reg) with either a soft faced hammer or the handle of a screwdriver - this will usually jar the brushes into contact with the slip rings - then if the red light goes out you know it is the brushes sticking.
90% of 'reconditioned' alternators simply are fixed and then painted - either brushes or a bearing will have failed and parts involved cost under $10, so a reco alt is generally just a repaired alt.