I've now had the honor of experiencing in-flight alternator failures in both PA-28 and PA-32R Pipers. I'm not too familiar with other types so maybe this doesn't apply to all aircraft but it's definitely applied to the ones I've owned.
Both of these aircraft had the three square orange annunciators.... VAC ALT OIL. In both cases the ALT light was so dim in daylight that it was barely visible. Even cupping my hands over it to provide shade it was barely possible to tell it was on. This will NOT get your attention in the event of a failure. In the PA-28 my first warning was my GPS screen going blank as voltage dropped too low for it to stay on.
In the PA-32R I had an EDM-800 engine analyzer that started flashing the voltage at me. I dropped the gear right away and flew about 30min in VFR conditions back home, didn't lose nav or comms the entire time. I had about 11.5-11.8V all the way to landing.
Anyway what I really wanted to get across is that annunciator light is basically useless. Unless you're watching your ammeter like a hawk you probably won't notice it moving from just above 0 to 0. That engine analyzer made a HUGE difference in detecting the problem quickly. If getting one of those isn't in the cards and you have a cigarette lighter there are digital voltmeters that will plug into them and have USB charging ports on them for very reasonable prices on amazon. Better than nothing, I'd suggest something especially if you fly in IMC or are flying a retract.