I think you have the idea right, dont try the disconnect though with the motor running.
A simple sign of a alt working is to have the lights on with the car idling. When you rev it up the lights will go a little brighter. That is a sign of a alt working. If the lights just continue to get dimmer with the motor running above 1500rpm, you have a charging/alt problem. I once had a problem with the thick wires from the alt to the cars elec system.
If the idiot light isnt working when you turn the ignition on before starting, the alt normally wont start to charge. It needs the current through the light to start the alt working.

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Grumpy Old Diesel Owners Club group

I no longer question authority, I annoy authority. More effect, less effort....

1967 230-6 auto parts car. rust bucket.
1980 300D now parts car 800k miles
1984 300D 500k miles
1987 250td 160k miles English import
2001 jeep turbo diesel 130k miles
1998 jeep tdi ~ followed me home. Needs a turbo.
1968 Ford F750 truck. 6-354 diesel conversion.
Other toys ~J.D.,Cat & GM ~ mainly earth moving