I think you should see the MAC-address of the Primary, and if you login to the switches you should be able to figure out on which physical port this Primary MX is connected to. If someone is at the location where the devices are, then maybe they could help you locate to which physical device the correspondig MAC-address belongs to through some detective work 🙂
I don't have any active warm spare configuration in my dashboard so I can't verify any setup at the moment..
Aouch, yeah this is not a scalable solution... Therefore you mentioned the API calls 🙂 It sounds strange that it doesn't show any Serial number on Primary MX? I know it did before, but it was a while ago..