There were a few mods that do this, but It looks like all the mods were broken by updates, including Valheim Plus. Valheim Plus included the feature 2 years ago but after it broke they did not get it working again so it was removed from the feature list.

However, you could use valheim plus to do something related. There is a setting which modifies how dark the night-time is. So, you can make it roughly twice as bright.
Heres what the config looks like:

[Brightness]

; Change false to true to enable this section.
enabled=false

; Changes how bright it looks at night. A value between 5 and 10 will result in nearly double in brightness at night.
nightBrightnessMultiplier=0

The cycle will remain the same in time, though. This mod just makes the night less dark so its easier to see. Hopefully somebody else comments with some insight into a currently working solution.