Probably the "Midnight Ride" of Paul Revere in 1775, the American Revolution, to warn re the British Army (or else Tam O'Shanter by poet Robbie Burns when he escaped from the witches!)....
Staying awake late into the night and losing sleep.
You'll be burning the midnight oil the night before a final exam.
Many U.S. taxpayers are burning the midnight oil on April 14th.