The manual says, in /usr/share/doc/links-0.96/manual-0.82-en/links-configure-other.html: 2.5.5 Terminal Options (in Links.cfg) When a user runs Links for the first time, the configuration file (.links.cfg) is created. terminal2 "xterm" 1 0 0 1 us-ascii Neither Links.cfg or .links.cfg are written, but ~/.links/links.cfg. The "terminal2" is not written, but "terminal" is written istead.
In elinks not even .links/links.cfg is written.