There must be a driver involved, or a module that has to be loaded.
Try first:

sudo modprobe -v sony-laptop

This will load the module. Then try the suggestions.

The description of sony-laptop explains the parameters involved:

$ modinfo sony-laptop

[...]

parm:           no_spic:set this if you don't want to enable the SPIC device (int)

parm:           compat:set this if you want to enable backward compatibility mode (int)

parm:           mask:set this to the mask of event you want to enable (see doc) (ulong)

parm:           camera:set this to 1 to enable Motion Eye camera controls (only use it  if you have a C1VE or C1VN model) (int)

parm:           minor:minor number of the misc device for the SPIC compatibility code, default is -1 (automatic) (int)

parm:           kbd_backlight:set this to 0 to disable keyboard backlight, 1 to enable it (default: 0) (int)

parm:           kbd_backlight_timeout:set this to 0 to set the default 10 seconds timeout, 1 for 30 seconds, 2 for 60 seconds and 3 to disable timeout (default: 0) (int)

So 1 to enable, 0 to disable.

Temporary solution:

sudo modprobe -v sony-laptop kbd_backlight=1

To turn it off:

sudo rmmod -v sony-laptop; sudo modprobe -v sony-laptop kbd_backlight=0

Permanent solution (always on when you boot):

echo "options sony-laptop kbd_backlight=1" | sudo tee /etc/modprobe.d/sony-laptop.conf

(You have to reboot for changes to take effect)