There are only 2 ways that the light would stay on with the ignition off

1/ power is connected to the thin wire at the back of the alt via the reg.
2/ there is power still connected to the down stream side of the ignition switch.

Disconnect the thin wire at the back of the alt reg. Put a volt meter on the wire, if 0volts then most likely reg problem. Put volt meter on tab on reg. If a few volts (dont need 12) then reg is faulty. If 0 then the problem is some place else, maybe the loom.
If when you test the wire you get voltage, then ig switch is bad or loom fault.

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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