Run 600’ of 2 core wire to the mailbox.
Connect to a standard magnetic alarm contact at the mailbox
Connect the other end (in the house) to a contact sensor joined to HE
That would work if you can easily hide the wire etc
1200' (there and back) is going to give you a LOT of voltage drop though. How many miliamps does a contact sensor put through the reed switch? (i've never checked). At 100mA you're going to get 76% voltage drop at that distance.
The only reason I asked was I had typed up the exact same post and was about to hit save. Then I thought of voltage drop. So i thought maybe you'd already considered it. No worries. It is a good idea to try. Wouldn't cost you anything...you can try it right in the house.
I thought about doing that --and probably would have done it if I had an available conduit. ( I have some going out to the road, but not over to the mailbox. Apparently, I wasn't thinking of mailbox announcers in the 1980s when I built the house.) But for <$50 I decided not to get into trenching. hhh.
Nope
However; the alternative would be to use 12vdc and a small low volt relay (taking into consideration the voltage drop) to open/close the contact sensor
I'd actually thought, use a 12 volt source out to the mailbox reed switch, then a voltage divider to send that signal into the contact sensor in the house. but that just gets REAL complicated.
I would just shove 12vdc to the reed switch and measure what comes back.. no calculations required for wire gauge etc
Then a suitable reed relay or transistor circuit to switch the HE contact
Well, yeah. If you want to go that route, if you used an Arduino or ESP board, you could probably get away with sending out 5v and using the standard analog input to measure the voltage.
Actually, i just checked....if you send out 5v, you would have enough at the end to still trip the digital input on an ESP board. you'd have about 2.5v. You wouldn't even have to use an analog translation.
However, in all this talk of the electronics, we've forgotten that this solution also means you'd have to bury 600 feet of low-voltage landscape wire. LOL
We could go on forever, but this doesn't sort out the OP’s problem as he has already said he is unable to run the cable - shame... it might be fun to try
@mbishop if you are handy with electronics (Arduino or ESP8266). You could create a notifier using a pair of 433mhz transceivers, a reed switch, antenna and battery on the mailbox side. It should be battery efficient as you can close the battery circuit using the reed switch. Therefore it's only on to transmit the "I'm open" signal.
Then connect the transeiver in the house to a ESP8266. Transceiver signal goes high and indicates the mailbox was opened. Then use the Hubduino or Tasmota firmware to connect the ESP8266 to HE.
The 433mhz transceivers are very cheap. Do you could test the distance easily. Also 433mhz is a long wavelength (when compared to other frequencies we have access to). The long wavelengths penetrate obstacles better. That's why 2.4ghz WiFi penetrates better through houses and has a longer range than 5.8ghz WiFi.
I built one of these with my Dad. But on the house side he tied it to the door bell. So the the door chime is ding dong and the mailbox goes dong ding!!!
Other ideas to throw out there for long range:
Use 433Mhz RF long range transmitter to signal a Sonoff RF 433Mhz Bridge (which can be HE integrated). I think that can go from 100m up to 500m (plenty)
Wait for Amazon Sidewalk (up to a mile?) and see if that can be integrated to HE.