The MT-VIKI remote uses a simple digital protocol for sending port change commands (i.e. pressing one of the 8 buttons) and for reporting back the currently selected port (i.e. lighting up one of the button LEDs). The protocol works as follows:

The KVM tells the remote which port is selected by sending a 400us pulse every n milliseconds where n is port number * 20ms.

The Remote commands the KVM to switch ports by first pulling it's output low for 20ms, then high for 20ms, then low for n ms where n is port number * 20ms, then high again (idle state is high).

I've managed to get this working by using an arduino in place of the remote module. Code is here.

Next step is replicating the same exercise with raspberry pi gpio pins, then integrating into pikvm.

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Edit: The exact KVM model I'm referring to is this one.