External source can only either be MoH or BGM , NOT BOTH.
Set your External source as BGM , then program the trunks to use BGM as MOH.
Program your trunks to use BGM as its MOH source
If you are using Direct In Dial you also need to program this in all relevant tables:
Now the user can dial service code 725 to enable / disable handset BGM
Or
Program a Key as Feature 04 ( BGM )