Since you tagged your question "Debian", here's a quick recipe that should solve your problem.
finder computers run the following (as
root, or use
sudo as/if necessary):
# apt-get install avahi-utils
Then, as long as the
finder computers are on the same broadcast domain (i.e. the same physical network), you should be able to use
avahi-resolve to resolve the IP address (either v4 or v6) of each host from the other.
For example, any user on
finder can resolve
lost, as follows:
$ avahi-resolve -4 -n lost.local
$ avahi-resolve -6 -n lost.local
$ avahi-resolve -4 -n finder.local
$ avahi-resolve -6 -n finder.local
Obviously, I have glossed over a lot, and a few little details could go wrong that prevent avahi from working correctly out of the box, but from my own experiments on a few different occasions, there's a good chance that it should all Just Work (tm).