What Gillnetter said does make sense, if that's what Bamako5 is denying.
When you remove "am" from "I am busy", it becomes nonsense, therefore "am" is not auxiliary in this sentence. When you remove "like" from "I like you", it becomes nonsense, therefore "like" is not auxiliary in this new sentence either.
"Am" is the main verb in "I am busy" and so is "like" in "I like you."
An irrelevant remark: as it was said in another thread, we don't use a period after "et" in "et al."