Gudrun Bühnemann is a Professor at the Department of Languages and Cultures of Asia of the University of Wisconsin-Madison. In her book, Mandalas and Yantras in the Hindu traditions (2003) there’s a chapter about the hexagram, where I found some info that was new to me (but I didn’t find an answer to the question about the origin of the Indian hexagram).
The hexagram (satkona, sadara, tara) - Begley  1973:85 notes that the word star, Tara, appears as a synonym for satkona
My Note (zeevveez): the sound of the word "sadara" id also close to he sound of the word "star".
 Begley Wayne Edison, Vishnu's flaming wheel: the iconography of the Sudarśana-cakra, New York University Press for the College Art Association of America, 1973
In Budhist Tantrism the word "evam" is thought to be represented by two intertwined triangles...Kolver discusses the shapes of the letter e and the va which were remeniscent of downward pointing and upward pointing triangles around the sixth century C.E. and were visualized as hexagram... when Vagra-yogini is described as situated “in evam” this means that she is visualized inside a hexagram.
In descriptions of the symbolic shapes (mandala) of the elements the hexagram represents the element wind.
In the hexagram the deities are often worshipped at the points of intersection of the two triangles…
In Budhist traditions hexagrams appear especially in mandalas of Vajra-Varahi / Vajra-Yogini.
According to Nath 1975-1976:78 the hexagram is also found in Indian temples, especially in Rajastahn were it is believed to have been associated with the worship of Siva and Sakti.
The hexagram appears in Islamic monuments of North India. Its center features a point (bindu) a lotus or a dancing peacock. (Nath 1975-1976:74-75).