The battery light [idiot light] has started to come on - the battery has checked out good with 12.6 volts with engine off and when running the battery stays the same 12.6 volts. Am I looking at an alternator problem or something in wiring for this problem?

Likely it is the alternator, possibly a separate voltage regulator if it has one. Usually there is a heavy black wire coming off the alternator. Check it for the 12.6 volts with the engine off. If not, follow it back to the battery checking connections all the way. Try to identify the smaller field terminal on the alternator. With the engine running, it should be hot. If not, trace it back as far as you can.

If that doesn't help, many of the DIY oriented parts chains will test alternators for free.