Could it be 'the dust that I eat back on drag'?

This assumes that being 'on drag' means riding behind the herd, where much dust has been stirred up by hooves.
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I listened to the Merle Haggard recording and was really put off by the imposition of all the Mexican sound on a song obviously being sung by a simple American white guy, probably from Kansas or somewhere similar.   
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Why is a guy who drives cattle called a drover, not a driver?