After reading up on the matter, here’s the rules: Its not about age, a player does have to be eligible for an NFL draft (or supplemental draft) and go undrafted before they can sign with any team they wish as a free agent. If they end up getting drafted by a team and refuse to sign a contract, they are re-entered in the draft the following season.
Regardless of the players age, the NFL would have a MASSIVE problem with players manipulating where they land if going through an NFL draft wasn’t mandatory.