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If it does have an IP address and is (perhaps occasionally) active you can run a capture on the network interface attached to it and filter on its MAC address, which you presumably have. Or if you don't and this is the only device on the network interface then anything coming in is from the device.
On the other hand, if it remains quiet, you'll have to see if you can provoke some response. Either by triggering something on the device which causes it to send packets, or if you're lucky it may respond to a broadcast ping.
If nothing else helps then a network scan, e.g. using nmap may help. Start with the usual suspects, as in, the private network ranges and go from there.