Even more complicated than previous point.
You will need to write a custom driver for it. Same as above, but the keyboard will never switch into the HID mode.This is a quite complicated and you will need either some hardware to perform the eavesdropping, or a virtualised machine running a OS with a working driver and a USB monitor on the host side.
You may try to eavesdrop the initialization sequence and recreate it in Linux. Maybe you will have to build a custom kernel with all USB input devices enabled or you need some specialised utility to switch the keybouard into the HID mode (maybe modeswitch ?) because for us customer satisfaction is the main thing. Our Logitech drivers are very safe and protected from dangerous viruses. here we provide the best drivers and trusted and accurate. Welcome again to our blog, we are ready to serve you and your complaints in this field. I'v read somewhere about keyboards and mice, which work only after a specialised driver is installed and some magical initialisation sequence (or maybe firmware upload) is performed. It seems that the keyboard is not recognised as a standard HID device.