AMP Light - what exactly does it indicate?

Last week, the AMP light came on, and it has been on and off over the last week of driving. Seems that if I get going for a while without stopping it goes off. Around town, the light comes back on for most of the time. My volt gauge is showing a notch over the middle line. Today I checked the amps with my multimeter while the engine was idling (1400, tho.. long story on the idle). I was getting a steady 14.38 amps. So.... it appears that the alternator is working fine, right? Is the battery going south? If the battery is ok, then what else causes the AMP light to come on? Oh yeah, at any given time when the car is off, if I can get 12.4x amps on the multimeter and the starter solenoid, so the battery appears to be holding a charge.

Today I went by the Zone to get the battery and alternator checked. They were so busy I had to wait about 25 minutes before anyone was free to check it. As it turns out, the battery is bad. That sucks, because I have to drop the gas tank to get the battery out. I hated Summit's battery relocation kit from the beginning. Seems to be designed by a 5 year old. Now I am really hating it. When I pull this battery out, I think I'm going to make my own battery box out of 1/8th inch steel and make it easily serviceable for future incidents.