I would like to say, "Yes, you must sleep." Would this be correct?
Ja, du musst schlafen.
The reason I ask is because I'm not sure whether the subject and verb are in the correct place. I know that the verb should typically be in second position whenever the sentence is declarative. Does this hold true for clauses as well as sentences? The verb is second position in its clause, if not its sentence, so I think it is correct, but I wanted to make sure.
Ja, du musst schlafen.
Would this be correct?
Yes this sentence is correct.
Does this hold true for clauses as well as sentences?
No. The rule is that the second element of a whole sentence is the verb of the main clause. Relative clauses have their verb at the end:
Weil du morgen gut ausgeschlafen sein sollst, musst du schlafen.
In this example the relative clause "Weil du morgen gut ausgeschlafen sein sollst" is the first element of the entire sentence. The verb "sollen" is the last element within that clause (because within such a clause the verb is found at the end). The second element of the entire sentence is the verb "müssen".
Ja, du musst schlafen.
When do words like "Ja" count as "elements" of the sentence?
A very good question. Replace the word "Ja" by the word "Klar" ("of course") and you'll get the following examples:
Klar musst du schlafen.
Klar, du musst schlafen.
In the first example the word "klar" obviously counts as "element" of the sentence while in the second example it obviously does not.
Both variants have the same meaning and (when using the word "klar") both variants are in use.
