How to identify the form and function of the word "that"?
Solution 1:
To presume that relative pronouns function as nouns and adjectives is faulty logic. They merely refer back to the antecedent, and the clauses they head are what really function as adjective clauses. And since conjunctions are merely connecting words, that as conjunction never refers back to antecedent as does the relative pronoun that. Once you go by this logic I'm sure you could tell one from the other lickety-split.
Thus,
This is the book that Bill wrote. (Relative pronoun)
But
It's unlikely that he will succeed. (Conjunction)