Locksmith here. In a pinch, I’ve ground the back of a jigsaw blade down, leaving just the teeth on the blade (short enough to fit above the key). Jigsaw blades, especially those intended for metal, are hardened and will easily bite into just about any key, giving enough leverage to pull out the broken piece.

My guess was wrong! My photo was also taken from Mt. Lemmon in Tucson. Great pic, BTW!

The landscape in your photo immediately reminded me of a photo I took in 2014, although I’m betting that yours was taken much closer to Phoenix than mine was.