Heaving-to is a good idea, so is catnapping at night and getting more sleep in daylight (when no fog).
If hove-to, when you go below it's not a bad idea to leave a light shining on your sails, whether flashlight or spreader lights, if your batteries will stand it. Makes you much more visible than just your running lights do.
And if you're on deck and someone's getting close, shine a light on your sails for the same reason.
Singlehanded sailing at night is like solo scuba diving. No one recommends it, but a good number of people do it. Me, I dive with a buddy.