What happens if you don’t sleep?

The description of a long rest says:

A long rest is a period of extended downtime, at least 8 hours long, during which a character sleeps or performs light activity: reading, talking, eating, or standing watch for no more than 2 hours.

A recent Sage Advice, while discussing whether elves need 8 hours for a long rest, also clarifies that a long rest need not necessarily include sleep, and that the only activity limited to 2 hours is the standing watch:

A long rest is a period of relaxation that is at least 8 hours long. It can contain sleep, reading, talking, eating, and other restful activity. Standing watch is even possible during it, but for no more than 2 hours; maintaining heightened vigilance any longer than that isn’t restful. In short, a long rest and sleep aren’t the same thing; you can sleep when you’re not taking a long rest, and you can take a long rest and not sleep.

Presumably, though, most humanoids need to sleep (and elves need to trance) to avoid exhaustion. Yet I cannot find any rules relating to applying levels of exhaustion to characters who neglect (or are unable) to sleep. I don’t think the forced march rules apply here, as long as the characters limit travel/adventuring to 8 hours/day and spend the rest of the day doing downtime activities and resting.

I am thinking primarily of a situation where hallucinations, nightmares, or a noisy environment prevent a character from sleeping when he or she attempts to do so.

What/where are the rules that require a character to eventually sleep or trance? And what are the penalties for not doing so. The sage advice says sleep is independent of rest, so what is the penalty for not sleeping if the character has taken a full long rest consisting of only light activity.