We spent the night camping with herders. This bird was there in the morning, on some rocks at the camp's end.
Doubt: could it be Calandrella brachydactyla, instead?
Large-crested male on ground, displaying to small-crested female, with a "dance" that involved the male splaying it tail and hopping backwards towards the female, starting from about 1-m away, and stopping when the distance between the two birds closed to about 10 cm. Then male flew back to its starting position, ruffled its feathers, splayed its tail, and re-started its display.
Larks are passerine birds of the family Alaudidae. All species occur in the Old World, and in northern and eastern Australia. Only one, the Horned Lark, is native to North America. Habitats vary widely, but many species live in dry regions.