Sleep

Where, if anywhere, are the rules for going without sleep? I hoped they would be in the PHB and/or DMG, but I can not find anything other than "needing sleep" and a little in the section about rests and constitution checks, and again for elves.

Xanathar's has a whole section on sleep. As far as going without:

A long rest is never mandatory, but going without sleep does have its consequences. If you want to account for the effects of sleep deprivation on characters and creatures, use these rules.

Whenever you end a 24-hour period without finishing a long rest, you must succeed on a DC 10 Constitution saving throw or suffer one level of exhaustion.

It becomes harder to fight off exhaustion if you stay awake for multiple days. After the first 24 hours, the DC increases by 5 for each consecutive 24-hour period without a long rest. The DC resets to 10 when you finish a long rest.

Xanathar's Guide to Everything

Also to add that in the PHB on p.177, under 'Constitution' checks, one of the listed examples that a DM may call for a Con role includes 'to go without sleep' - which I've actually used before. 

Now I'd refer to the XGtE rules.

Super necro thread, my bad.
What happens when a creature doesn't need to sleep, do they ignore the saving throw, do they have advantage, do they roll like normal, what happens?