One of the glaring bugs of macOS Mojave’s initial release is that you can’t adjust the brightness of an external display using the brightness keys. Nor can you do it from System Preferences. But you can adjust it by downloading Brightness Slider from the App Store. It’s free and it works. Hat tip to Jreinhal.
Update December 24, 2018: I noticed last week that this bug is now fixed. By pressing F1 and F2 on my bluetooth external keyboard, I can adjust the brightness of my external display.