Every year players become eligible for the National Baseball Hall of Fame for the plain and simple reason they retired 5 years earlier. That’s the about the only simple part of the process. To be enshrined forever they need to get 75% of the voters to say yes. If they get between 5 and 74% of the vote they are allowed to remain on the ballot for the next 10 years. If they get less than 5% they fall off the ballot FOREVER!
There is an ass ton of politics involved in this process. Most of it revolving around biases on the writers. I’m only going to address those to say that they too often get in the way of accurately reflecting who indeed should be a Hall of Famer or not. And, each voter only gets 10 votes. So that totally makes it more political.