I think you're right, about when the ignition warning light extinguishes. It was always in the live feed to the alternator rotor windings in days gone by. when you switched the ignition on, current would be fed to the brush pack and thence to the slip rings and rotor windings (to establish a magnetic field) from there it went through a regulator and to earth. As the alternator revs increased so too did the output from the main windings which would oppose the current being fed to the rotor via the small connection on the alternator. As output from the main windings increased, because it was in opposition to the battery feed for the rotor a point was reached where there was insufficient differential between the two to light the little red light on the dashboard. In practice alternator output only had to rise to about 10 or 11 volts to reduce this to the point where the ignition light wouldn't illuminate. So, in "real life" the alternator could produce enough to cancel out the dashboard light but still not actually be charging the battery. I'm not entirely sure if this is so with "Smart" alternators where regulation/charging control is handled by a dedicated ECU?Don't agree.
I had battery issues from the day I bought my 500 twinair, changed batteries, alternator, earth straps, negative battery terminals, and not once did the light come on on the dash. IMO, I think its solved now that I put another earth able on (link below), I've not had a peep out of it, regarding electrical issues.
Another Earth Cable
Ralf comments above about the head lights light going dim and bright. This is an interesting one for "oldies" like me. Back in the days of dynamos they could not generate enough current at tick over to do much about providing a charge. So, one of the "classic" ways to check if charge was being applied to the battery was to switch the headlights on with the engine at idle RPM and observe headlight brightness against a wall or other suitable surface. - at tickover the system would be running at battery voltage of around 12.5 volts. Then lift the revs to a "fast idle" maybe 1500 to 2000 rpm whereupon the dynamo would provide charge and lift the battery voltage to 13.5, maybe 14.5 volts which would result in a noticeable brightening of the lights - job done, if the lights got brighter you could be pretty sure the dynamo was charging. Unfortunately this doesn't work so well now a days because alternators charge quite strongly even at idling rpm so revving the engine doesn't cause a rise in output sufficient to brighten the lights. Checking with a voltmeter is definitely the way to go on modern vehicles, especially as you can now buy a cheap but adequate multimeter for chicken feed. The Aldi/Lidl offerings are pretty good.