If I'm not mistaken, ARP could be used to receive a MAC address of a machine. If you are connected at the data-link layer, I believe you can execute `arp -an` on a Linux machine to retrieve the MAC addresses of connected devices.
I've only used it to retrieve the MAC address associated with IP addresses, as that's what its usual function is - however due to the connectivity being over layer two, and that it uses the Ethernet broadcast address (FFFF.FFFF.FFFF), it should hopefully be able to retrieve the MAC address alone without an associated IP address.
I'm not actually able to test the above theory, but please let me know if you have any luck.