He will support whichever candidate wins. (source)
This sentence strikes me as missing a relative pronoun. I thought it should read:
He will support whichever candidate that wins.
Per relative pronoun rules, I thought "that" can be left out when it is the object of a relative clause, e.g. "Take whichever book you want.", not when it is the subject.
In order to parse the first sentence, I am trying to think of an equivalent for the adjective whichever. Dictionaries have "no matter which", but this substitution seems to work with such sentences as
Whichever (No matter which) job you take, starting out will be hard.
But not with the sentence at issue. So how should I understand the structure of that first sentence? Am I correct in saying it is missing "that"? What would be a working multi-word equivalent for whichever (so that I can better parse such sentences)?