So, the current state is:
Before @anthony93 and @xircon kindly offered their script and unit solution I had tried:
echo 2 | sudo tee /sys/class/leds/platform::kbd_backlight/brightness
That turned on the keyboard backlights, but at reboot this setting was reset to 0, hence the backlight was turned off again.
I also tried:
brightnessctl --device="vendorname::kbd_backlight" set some_value
That gave the same result: reset at reboot.
I’ll now try the unit file.
I agree with @ricklinux that this should not be necessary, but having tried everything else I think the unit file is worth the effort for me.