Problem with charging system?

Driving down the road I'll occasionally get three red lights on my dash lighting up (Brake, A/T and Battery), a soft glow to start with and then getting brighter. At the same time the voltmeter slides down from its normal 14 volts or so down to 12 or just under. If the headlights are on they dim a little, if the heater blower is on it slows a little, dash lights dim a little yet everything still works as it should. Anywhere from 30 seconds to 5 minutes later the three red lights go out and everything is back to normal.

The only other problem I've had (my guess is that its related) is a couple of times when I've unlocked the truck (with the key, as I don't use the remote) the alarm has gone off. Mind you, it wasn't set to begin with and almost never is. The remote would not stop it, nor would the silence button. Had to wait out the full alarm cycle. Both times I then got out, locked it with the remote, unlocked with the remote and all was good.

Ideas anyone?

Thanks,
Mark