Bat
All Eocene bats had long tails. This feature is also found in early flying insects in the Carboniferous, in early pterosaurs and in Archaeopteryx and other dinobirds. The tail helped to keep their flight stable, which means it kept on course, and did not dart about much. To dart about quickly requires special advanced brains and reflexes, which later bats, birds and pterosaurs had, but early ones did not. It requires more brains to control unstable flight than it does for stable flight. That early bats had long tails was predicted by John Maynard Smith before any fossil early bats were found.