No the radio should go off with the key.

You will need a wiring diagram to follow the logic. It will be easier to just pull the diode and check it. Diodes are checked with an ohm meter. They should look like a short circuit one way and an open circuit the other way.

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Steve Brotherton
Continental Imports
Gainesville FL
Bosch Master, ASE Master, L1
33 years MB technician