That's odd. Audio system mute issues from the dealer installed car phones have usually affected the sound from the radio, cassette player and CD player equally -- at least that is what has been reported in previous threads. Usually disconnecting all the phone system components will resolve the problem -- on some Lexus phone systems, two connectors have to be plugged together after disconnecting them from the phone ECU in the trunk. Yours is the first time I've heard of anyone having to unplug a connector from the head unit to resolve this type of problem.
To illustrate my point, several of us on this forum have attached the mute wire on aftermarket phone kits to a mute pin on the factory prewire phone harness -- when a call is in progress on on our aftermarket phone systems, the audio system is muted regardless of whether the radio, cassette or CD is in use.
In case you don't already have it, attached is the full audio system diagram for a 1994 LS400 Nakamichi system.
Does anyone know the location in the vehicle of the car phone tranciever?