Interesting. The pet friendly settings might be useful in my house. A couple of thoughts. This sensor wants 12 volts. I have had bad luck with the cheap Chinese Pro-Minis I normally use. They advertise being able to use power up to 12 volts, but they fail quickly at that voltage. You will probably need to power the arduino differently from the sensor. I'm not that familiar with the Mega 2560, but it appears to have several additional interrupt pins over the regular arduinos. You would just have to pick one and use that in the software. Did a quick google and someone said the two "T" pins are tamper detection. The NC are motion detection. The tamper detection just tells you if the sensor case has been opened. The two NC terminals appear to be a normally closed switch contact. You could use a simple button setup like this: https://www.mysensors.org/build/binary This setup doesn't use interrupts and instead polls the switch pin. The down side is you will not be able to sleep the node. There may be better ways, but the sample above would give you a quick way to experiment with it.

UPDATE: I power cycled the board by physically removing the USB power/data cable and the board came up on the network + MQTT session to the broker was established!! For what it's worth and for future reference if anyone finds this thread: It appears the official MySensors Hello World ethernet gateway basic tutorial works great for the Mega/2560 board paired with a 5100 Ethernet shield.

You don’t need MySensors for this, PubSubClient will do what you need.