You need to register the ‘Communication Option Type’ Lookup in the ‘Lookups’ Section to be able to manage them for both ‘Contacts’ and ‘Accounts Section’.
To do that click ‘Add’, enter the ‘Communication Option Type’ into ‘Name’ and ‘Object’ fields and click ‘Ok’. If you get any warnings – just ignore them:
After this, you will be able to ‘Open’ this Lookup and Add\Edit\Delete the values.