The simplification of an animal may be due to the ancestors of that animal having taken to new habits of life. ~ Ray Lankester
Convergent evolution is different than re-evolution. In re-evolution (short for reversion evolution), a genetic expression previously abandoned is re-enabled. The reactivated trait is an atavism: reversion to ancestral type.
The evolutionary throwback of atavism comes from gene conservation. Mathematical modeling suggests that atavism may be had within 6 million years. After 10 million years, an unused gene is unlikely to be functional. Some genes are conserved such that no such expiration applies.
Embryos of various species display ancestral traits. Human fetuses have a tail. Such features typically disappear during development, but an atavism leaves an ancestral feature intact.
In a Lamarckian way, traits that no longer serve a purpose are minimized in time as a process of subtractive adaptation. Gene conservation long leaves the option open for later reversion.
Reversions regularly occur. The snake, which lost its lizard legs and went back toward worm form to get somewhere, is exemplary. Snakes retain the genes for legs. They simply lay dormant.
There are dozens of lizard lineages that have lost their limbs. ~ Australian evolutionary zoologist Michael Lee
Snakes also illustrate that supposed examples of atavism are often facile, in singling out a trait while ignoring others that are invariably coupled to the suite of changes that organisms undergo in adaptive transformation. Snake descent was much more complex than mere reversion evolution.