For 4 plus years we had our phone lines set up so that if someone was talking on the main line, the call would go to the secondary line and allow someone else to answer the call. If there was no one available to answer this call, after about 3 rings, the call would go to voicemail. We have a fax machine on this secondary line that we only use to send faxes but never receive faxes. The fax machine is set to not pick up until after 4 rings. No one ever sends faxes to this number because we also have a separate virtual fax number that receives faxes, converts them to PDF and sends to our inbox. For years we have had the phone lines set up this way. We recently moved to a new location. I have had numerous issues with trying to get the phone lines set up like before. There was one customer service guy that finally figured out how to set them up. It was great, everything back to normal the way it used to be.....then for some reason, Comcast service went out for 3 hours last week and now I can't get anyone to figure out how to reset all of this because for some reason it stopped working,,,,guess because of the outage. I am about at wits end and soooo tired of calling Comcast and trying to explain what I want and being told it can't happen. It happened for more that 4 years! Everytime I talk to a customer service rep they tell me something different. It is about to drive me crazy!!!!!!!!!!!!!!!!
" For 4 plus years we had our phone lines set up so that if someone was talking on the main line, the call would go to the secondary line and allow someone else to answer the call. If there was no one available to answer this call, after about 3 rings, the call would go to voicemail. "
It may be prudent for you set up up your FAX machine to pick up after 6 rings. However, if this cannot be done then in order to implement your specified above, it would be necessary for your second telephone number (TN) line to be specifically programmed using the Call Forward No Answer (CFNA) after 2 rings, to be safe to not go over 3 rings for FAX inadvertent pickup after 4 rings. Sometimes the Telephone switches even though programmed to 3 rings can trigger an extra ring and for you this will not work if your FAX will pickup at 4 rings. This is why I recommend 2 rings before being CFNA to your first TN Voicemail after no more than 3 rings.
I would actually make sure you are not in a standard hunt group structure and manually program both of your 1 and 2 TNs to be able to work and meet you business needs.