You keep responding that Radio Buttons aren’t an option but the reality is, what you are asking is exactly what a RadioGroup of Radio Buttons is designed to do.
You could do it with an Array of Buttons and I could explain how you’d do it but effectively I’d be explaining to you how to write a RadioGroup class which is pointless.
If ‘the requirement’ (which you haven’t explained) doesn’t want the default little circles used for RadioButtons then derive your own RadioButton subclass with a custom graphic which looks exactly like a normal Button then create a RadioGroup to handle everything else.