What does it mean when the text says saints like Sai Baba 'place their feet on the head of Time' and are untouched by birth and death?

This powerful imagery signifies complete transcendence over the mortal cycle. Chapter 43 explains that those who 'kill death' and control their own incarnation do so for the welfare of their devotees. For them, birth and death are considered 'false imaginations.' Sai Samarth, being the Supreme Brahman, is inherently devoid of bodily impulses and consciousness. His existence is not defined by the body, which is just an adjunct. He can wander in an invisible form as part of his 'spontaneous play of Yoga.' Therefore, he is beyond the reach of time, physical illness, and mortality, always existing in his true, unmanifest self while remaining imprinted in the hearts of his devotees.