Elecom doesn't even try with their firmware. They send an identical HID descriptor regardless of what the device actually supports (x +y scrollwheel, 5 other buttons). Here's the linux workaround:

https://code.woboq.org/linux/linux/drivers/hid/hid-elecom.c....

If you use a recent Elecom device and an LTS linux kernel you need to patch your kernel just to get the buttons working right!