In the exclamation That you be happy! what part of speech is the word that? Is it a conjunction via ellipsis, i.e. "(I wish) that you be happy!" If yes, then does this poke a hole in the idea that subordinating conjunctions necessarily introduce subordinate clauses?
6IMO, "That you be happy!" is not grammatical in English. If you've found a speaker (even yourself) who uses such constructions non-jocularly, we'd need to know more about the grammar of "that" in such a dialect. For example, maybe in that dialect, "that" is not a complementizer.– user6726Sep 22, 2017 at 16:58
This question belongs on english.stackexchange.com– MitchSep 28, 2017 at 23:27
ktm5124, IMHO your question is related to linguistics. You have only one comment, pointing out that it's not 'grammatical' (yeah, a typical English Stack Exchange answer, that is, having prescriptivist leanings) and one answer pointing out that it's a fragment, not a sentence. Neither is correct. 'That you be happy!' is valid English, and if anyone wants to say it isn't a sentence then I challenge them to define what a sentence is. It is illocutionarily restricted in its use (used for wishes or toasts, accompanied by gestures), but that doesn't disqualify it from being valid English.– BathrobeNov 27, 2018 at 9:42
Your phrase is a fragment (not a sentence). It might occur as the answer to a question ("What do you want?"). 'That' is a complementizer -- it makes 'you be happy' the complement of 'what'. This is similar to the demonstrative pronoun function of 'this' or 'that', except that the antecedent is a phrase rather than something in the external environment.