The short version:
My battery warning light comes on dimly when the car is idling, along with the parking brake light and the brake failure light. Giving the car just a little bit of gas (say to raise the RPM to 1100 or so) makes them all go out. The car has a new alternator, what else might the problem be?

The longer version:
A couple of weeks ago my battery light started coming on (but no other lights). Over a few days it got progressively brighter, and revving the engine didn't impact it. When my car started to crank slowly I cleaned all the connections at the alternator, and the light didn't come on for a while. The car has ~250,000 miles on it, and as far as I know it might have been the original alternator, so I ordered a replacement, figuring it's better to be safe then sorry. The replacement I ordered was a Bosch reman AL55X, which has a tad higher amperage output than the stock unit. My light started to come on again last week, so I put in the new alternator. The first time I started it up there was a noticeable improvement (previously I'd have to blip the throttle to get all the warning lights to shut off, this time they all went right off). The next time I started it up those warning lights stayed on again until I blipped the throttle, and at idle my battery warning light stays dimly lit, along with my parking brake and brake failure lights. Like I mentioned above, raising the revs just a bit will get the lights to go out, but as soon as it's back to idle they come back on.

The replacement alternator is a quality Bosch unit, so while anything is possible, I'd like to know if there are some other things I should look at or test before sending it back. Could it be time for a new battery, or new belts? Something else?

Thanks for the help as always!