1996 Nissan Sentra brake and battery lights on

Driving around the city the heater fan will sometimes speed up a bit and then both the brake and battery warning lights come on.
I took it in to a friend who checked the alternator and it was charging at the time he checked it - although by then the lights had gone off and all seemed back to normal. Also he said the battery was giving out a full charge of 14? Volts. He cleaned up the battery posts and sent me on my way, warning me to get to a mechanic fairly quickly if the warning lights persisted and if the wipers, radio etc showed signs of slowing down or dying.

This has happened intermittently over the last 4 or 5 days. Today the lights stayed on much longer. While they were on, I turned on the wipers and they were slower than normal. I also noticed today that there is also an audible click, like a relay, coming maybe from somewhere over by the glovebox area when the warning lights either come on or go off again. I pulled over and revved the engine in 'Park' and the lights went off and stayed off for the rest of the day.

There seems to be no trouble starting the car so far, but I am concerned since we've had a lot of snowstorms and freezing weather here, and I don't really want to get stranded.

Any ideas? I don't really want to replace alternators and batteries just to try and chase this down.