It should be possible to control the visibility of this field with section access if you filled there the field OMIT with Email or leaving it blank based on the data in BUSINESS_GROUP: Introduction to Section Access.
Now I understand what do you want to do but it's not possible with the "standard" logic of section access which allowed the visibility of a column and/or a record for an user or not but nothing in between them.
This means you need some additionally measures to get it. This could be to use two different mail-fields and depending of which field is available within the datamodel it will be displayed within the UI (the field could be replaced through a variable in which such a check is applied). Quite similar is the approach of duplicating the records and one record has a mail-value and the other is blank and per your field BUSINESS_GROUP you controls which of the records will be reduced.