I am curious about how the extender works, it may help me narrow down where my drone crashed.

Does your extender have an ssid or allow your phone to connect to it without the phantom on? When I lost my phantom I drove up and down the steet with the controller, extender and my phone. I was hoping I would be able to find the phantom wifi again and at one point I did. I tried to open the camera app but I kept getting "connection to phantom failed". It did not seem like I could change any of the options in the app and it did not update the phantoms location under the find my phantom. I just assumed the phone connected directly with the extender since I was not able to see anything or control anything from the app.

Tested when I got home and yes you can connect to the extender when your drone it off.....the extender broadcasts the ssid

There is a "Find my Phantom" feature in the DJI App but it's pretty much useless if the battery pops out in a crash or you've otherwise lost the signal connection to the Phantom.  You may want to look into some of the third-party GPS trackers or loggers that you would attach to the Phantom.  Most have an independent power supply so they would still work even if the Phantom is damaged.

Yup, in hind sight an external tracker should be standard equipment for something like this.