I had a similar idea, for a fax/answering machine switch,
to put both machines on one line.  You order distinctive
ringing from your phone company.  This is $3/month here.
You get a second (unpublished) phone number.  When
someone calls this number, your phone rings with short
rings instead of long rings.

You set up your answering machine on 4 rings and your fax
on six rings.  You'd give out the new # as your fax #.
A device would measure the length of rings.  When it
detects a short ring, it turns off your answering machine.
Five rings later your fax picks up the call.

This should be cheaper and more elegant than the $80
switches now available.

But that's not what I did.  I'm giving out the new
# to my friends and customers.  This should leave the
old # for telemarketers, etc.  I won't pick up the
phone when I hear the long rings.