Well, his son Charles went into politics, so there's that.
As for Thomas... perhaps he runs in New Jersey while in Menlo Park, in something akin to how Woodrow Wilson tried to persuade Henry Ford to run in Michigan (and Ford and Edison were neighbors at their summer homes in Florida, and was not Wilson governor of New Jersey, after all?). Edison did, after all, accept a political appointment to the Naval Consulting Board -- perhaps he finds himself proposed as Assistant Secretary of the Navy, and then from there he develops a taste for politics. His views on violence might have impeded him (while he worked on weapons, he claimed he worked on only defensive weaponry), not to mention the allegations of atheism.