Battery likely won't fix it. I suspect if it was the battery, you'd get a light under more conditions than you are. One thing to do is find a place with one of the computerized battery testers. These do allot more than typical load tests. (They can also test severely discharged batteries and tell you if they are bad before you try to charge them and maybe have it explode in your face.)
1. Check for recalls. Make sure any are done or get them done. GM has a ton of truck recalls. Many of them for electrical problems.
2. Check the wiring VERY carefully. If there is damaged/failing wiring, it can make the alternator shut off intermittently.
3. Replace the belt and the tensioner if it has one. If either are letting things slip, the alt light can come on. (This is possible for several reasons. More in a sec.) You have enough years and probably miles that the tensioner can be weak/sticking. Use a Dayco Polycog or Gates belt.
4. Find out exactly which type of alternator and what regulator is in it.
GM changed to what is called an ASR a number of years ago. Short for Application Specific Regulator. (Yes, I thought it was a dumb sh_t name too.) The ASR is often tied much tighter to the ECM/PCM than the ones used in past SI or CS alternators ever were. To the point that the PCM actually turns the alternator on/off. If the PCM or wiring to it have problems then the alternator signal could actually be false. Meaning the alt may be shutting off but there's not a damn thing wrong with it.
If the parts books don't say... look at the wiring charts. A typical CS is wired as shown in my cave with 2 or three wires. Ones that are tied to the PCM can use similar wiring, use the 4th wire and maybe more. You're looking for any of the side terminals going to the ECM/PCM. If it uses 4 or more wires on the side, then it is pretty certain to be tied to the PCM. (A CS alternator using the P terminal is connected to the PCM. No other reason to use it that way.)
Belts are even more important with ASR, or even standard CS family alternators, when wired to feed the Tach (P terminal) signal to the PCM. If the belt slips then the alternator may be on but not in the speed range expected by the computer. The computer may then turn on the Alt/Bat lamp, or shut off the alternator (Which should turn on the lamp), depending on programming and wiring.
Another possible test... if the alternator is connected to the PCM... see if there are any codes stored. A PCM controlling the alt may not have turned on the MIL lamp when setting a code for this sort of problem since the Alt/Bat light is on.
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Dr. Ian Malcolm: Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.
(Jurassic Park)
The Ogre's Fiero Cave (It's also at the top of every forum page...)