1. I'm allowed to make grammar mistakes
2. I was actually correct on this one occasion; I could say 'Me and Switch' or 'Switch and I', technically old people are allowed to hit me and say 'It's Switch and I!!!' if I use the former.
Oh and as far as I know, "Him and I" is used in sentences where the "Him/I" is the subject of the sentence, while "him and me" is used if him/me is the object of the sentence.
In your case, "you" was the subject, "Switch and I" the object, so it should have been "Switch and me".
Now if you said "Switch and I want you to join" it is correct.
Or am I completely off track here?