https://mods.factorio.com/mod/Clockwork

Does this mod override Clockwork's settings to create the seasons over a standards day cycle?

Not tested.
I want to add an option to disable seasons, then they can be used together.

Is there a way I can have this mod not override any/most changes made by Clockwork, and only change the light level of the night? Clockwork has a problem with the night's light level: it's either too light or too dark, and also has instant dawn-skip if night is too light.

Alternatively, can you show me how to use Night Brightness in place of Clockwork? I am using an 8 hour day/night cycle (60x multiplier) with equal day/night lengths but Night Brightness settings are very different and (to me) slightly confusing.

You can set it just with console:
https://wiki.factorio.com/Console
https://lua-api.factorio.com/latest/LuaSurface.html#LuaSurface.ticks_per_day

60 ticks * 60 seconds * 60 minutes * 24 hours = ticks in day:

/c game.player.surface.ticks_per_day = 60 * 60 * 60 * 24

You can set the time of dusk, dawn, evening and morning (0.25, 0.45, 0.55, 0.75)
https://lua-api.factorio.com/latest/LuaSurface.html#LuaSurface.dusk
https://lua-api.factorio.com/latest/LuaSurface.html#LuaSurface.evening
https://lua-api.factorio.com/latest/LuaSurface.html#LuaSurface.morning
https://lua-api.factorio.com/latest/LuaSurface.html#LuaSurface.dawn

https://wiki.factorio.com/Time

/c 
game.player.surface.dusk= 0.25
game.player.surface.evening= 0.45
game.player.surface.morning= 0.55
game.player.surface.dawn= 0.75

The last thing is a min_brightness

https://lua-api.factorio.com/latest/LuaSurface.html#LuaSurface.min_brightness

/c game.player.surface.min_brightness= 0.15