If you have a dedicated line for the FAX, why not program the system to have the FAX line appear WITHOUT ring on the phone extensions, and appear WITH ring on the FAX extension (but the other lines WITHOUT ring for the FAX extension).
Then set auto line select for the phones to pick the FAX line last, but the FAX extension to pick the FAX line first.
Now you have an extra line for outgoing calls on the phones, incoming calls to the FAX only ring to the machine, but you get the line lit up when in use. If someone is talking on the FAX line when you need to send a FAX, the machine will automatically pick a voice line for outbound.