Buick century high blowers wont turn off, not the relay?

It sounds like a faulty control module to me. It should be possible to verify that’s the problem before replacing it, but it seems like the consensus here from the experienced folk is the module is almost certainly the problem so save the expense of testing and just replace it. I’m not keen on that idea and if I had this problem myself I’d probably do the necessary testing to prove it is a faulty module first. If you do decide to replace the module, suggest to retain possession of the currently installed one.