There’s not much to say here. Ago is not related to “a go.” I.e., it would not be equivalent to say “I’ll have a go at it” or “I’ll have ago at it.”
Nor would it be equivalent to say “he had a go at her” or “he had ago at her.” That would be something completely different.
In both of the above examples, I can’t think of any way to make the “ago” version of the example make sense. So don’t use it unless you can find a way to make sense of it.
Instead, ago is an adverb that means in the past. Simple, huh? Like I said, there’s not much more to say about it.