OK, there is no such thing as a "true" relative pronoun. Categories like this are not set by god or law, nor discovered by science. They're descriptions, and they don't describe everything.
The phrase relative pronoun refers to pronouns that occur with relative clauses. Not just any pronoun, but special pronouns that are, um ... relative to relative clauses. And, in English, certainly there are some. But they're busy words, and don't all relate only to relative clauses. So, what's a relative clause? No relative clauses, no relative pronouns, after all.
A relative clause is a clause -- that is, a simple sentence, with a subject and a verb, and maybe lots of other stuff -- that modifies a noun phrase. That makes it an "adjective phrase" in some grammars, but I don't like that term. It's not the only kind of clause that modifies noun phrases, but it is the most common, and therefore it's got the most confusing grammar.
Relative clauses come after the head noun of the clause they modify; this noun is called the relative clause's Antecedent (from Latin meaning 'coming before'). Relative clauses are distinguished from other types by having some coreference to the antecedent noun phrase. The relative pronoun is what substitutes for that reference; but sometimes the antecedent isn't a person or a thing, so it isn't a pronoun.
- the man [who Bill pointed out to me]
- the drink [which I bought at the bar]
- the time [when the clock stopped]
- the room [where she shot him]
In all of these, that can be used instead of the wh-words. And in all but the last one, the relative word (pronoun or not) can be deleted:
- the man [Bill pointed out to me]
- the drink [I bought at the bar]
- the time [the clock stopped]
And then there's how and why. Both are severely restricted in relatives: why can only modify the antecedent reason, and how can't appear at all as a relative word, though it can be deleted after the word way, manner, and a few others. That may be used instead, in both cases.
the reason [why he did it] (but not purpose, intent, or any other noun)
the reason [that he did it]
the reason [he did it]
the way [that he did it]
the way [he did it] (but not *the way how he did it)
If you want to call that a relative pronoun, go right ahead; it can apply to anything, just about, certainly to nouns. It's really the remains of a complementizer that used to occur in tensed clauses (and still does with certain verbs -- He thinks that shaving is silly), but got stuck with some of the jobs in relative clauses, which have a lot of complexities. Whether it's part of the true, the blushful list of relative pronouns is not for me to say.