Anyone have a clever solution to this problem...

I have a one-line telephone, but two telephone lines in the house.

Is there some way, perhaps with relays to recognize which line is
ringing and have the one-line phone connected to the ringing line?

(It's a honey-do problem... you know... "pretty phone, don't throw it
away" :-)

Radio Shack used to sell such a device. IIRC it's basically a
latching relay with the coil(s) activated by the ringing current.

Dunno if they or anyone else still markets something like this... I
bought ours back in the late 1980s.