eterm-color: Unknown terminal type

It does seem that you've seen the following information already, so it might not help, but it's probably worth reiterating.

The Emacs Wiki explains that you should copy (or symlink) the eterm-color and eterm-color.ti files from the /usr/share/emacs/xx.x/etc/e directory on your local system to the ~/.terminfo/e/ directory (or alternatively, system-wide at /usr/share/terminfo/e/).

Of course you can also do likewise on any remote host you need to connect to.

On Debian-based systems you administer, you can apt-get install ncurses-term, which includes /usr/share/terminfo/e/eterm-color.

With regard to the details in the question, note that if you didn't already have a ~/.terminfo directory then cp -r /usr/share/emacs/21.4/etc/e ~/.terminfo would not do what you intended it to do. It's not clear whether or not that was the case, but it may explain why it didn't work? You need the eterm-color files under a ~/.terminfo/e/ directory; not directly in ~/.terminfo/.

(n.b. Personally I always just install ncurses-term, so I can't vouch directly for the ~/.terminfo approach.)