I made some progress with this. In Devuan, I cat'ed all events in /dev/input/ to see which one produced output when I pressed Fn+F4.
I found that 'cat /dev/input/event0' produces output when I press Fn+F4. Interestingly, no other mouse or keyboard activity causes output from event0.
So I tried to figure out what this event0 refers to:
Devuan$ dmesg | grep event0
[ 7.148279] elogind[2005]: Watching system buttons on /dev/input/event0 (Sleep Button)
Devuan$ grep event0 /var/log/Xorg.0.log
[ 9.236] (II) config/udev: Adding input device Sleep Button (/dev/input/event0)
[ 9.237] (**) Option "Device" "/dev/input/event0"
[ 9.238] (II) input device 'Sleep Button', /dev/input/event0 is tagged by udev as: Keyboard
[ 9.238] (II) input device 'Sleep Button', /dev/input/event0 is a keyboard
[ 9.260] (**) Option "config_info" "udev:/sys/devices/LNXSYSTM:00/LNXSYBUS:00/PNP0A08:00/device:2a/PNP0C09:00/PNP0C0E:00/input/input0/event0"
[ 9.262] (II) input device 'Sleep Button', /dev/input/event0 is tagged by udev as: Keyboard
[ 9.262] (II) input device 'Sleep Button', /dev/input/event0 is a keyboard
Wow, so it seems that the Sleep Button is an input device all by itself!
Does the above suggest a way for TCL11 x86_64 to be able similarly add the Sleep Button as an input device?