Force GNOME Night Light to stay on and never turn off

The "native" way for Gnome Shell to always keep your nightlight color on involves to access some hidden options in dconf-editor. dconf-editor is not installed by default on Ubuntu 18.04. You may need to install it first.

• Open dconf-editor and navigate to the key /org/gnome/settings-daemon/plugins/color/
• Set night-light-schedule-automatic to false
• Set night-light-schedule-from to 0, and night-light-schedule-to to 24 (or any value higher than this)

You can also adjust your color temperature there.

In Ubuntu versions later than 18.04, these settings are exposed in "Settings", under "Displays".

Another alternative is sct which you can install with sudo apt install sct.

$ sct -h
Usage: sct [temperature]
Temperatures must be in a range from 1000-10000
If no arguments are passed sct resets the display to the default temperature (6500K)
If -h is passed sct will display this usage information
$ 

Putting sct 3500 or whatever other value you prefer in your autostart should do it.

I was similarly looking for a way to keep it on at all times but didn't see a way through the GUI. The other answers work but I found a simpler way to enable it via terminal without having to install any additional tools:

gsettings set org.gnome.settings-daemon.plugins.color night-light-enabled true
gsettings set org.gnome.settings-daemon.plugins.color night-light-schedule-automatic false
gsettings set org.gnome.settings-daemon.plugins.color night-light-schedule-from 0
gsettings set org.gnome.settings-daemon.plugins.color night-light-schedule-to 24
gsettings set org.gnome.settings-daemon.plugins.color night-light-temperature 5000

To get an idea of temperature value ranges, Redshift uses default values of 3700 at night and 5500 during the day.