I am the dramaturg for a production of Sam Shepard's play "True West." The characters in the play always refer to living "on the desert" rather than "in the desert". Likewise, the say things like "out on the desert you get to know what's real." My actors struggle with it not sounding natural to them to say "on the desert".

Researching the two phrases online has been difficult since desert can be an adjective ("on the desert island") but I have found many instances of apparently standard use of "on the desert" as Shepard uses it in the play. For example, there is a Johnny Cash song called "Lost on the desert."

We use "on" for vast, flat, boundary-less geographic locations in other instances: "on the sea/plains/mesa/prairie" but not usually for desert.

So can someone shed some light on this?

Is this a regionalism? (the play takes place in Southern California, USA)
Is "on the desert" archaic or waning in usage?
Is there a semantic difference?

It's a minor point in the script, but Shepard is always so specific in his choices, I know there's something here. Any help would be appreciated.
Thanks!
Stuart