Wherever the dots appear fill in one name of the deity. Of course you can invent gayatri for them by interfacing three names of the deity with the four words of gayatri: 'Vidmahe', 'Dhimahi', 'Tanno' and 'Prachodayat'. Sangili karupan and muniappan are typical village deities of tamil nadu and hense no gayatri for them. there are no gayatries for typical dravidian gods.
Gayatri mantra originally is of Vadic and Arian origin for sun worship ( Savita, savitri) latter extended to various deities of northan sanscrit hinduism - gods refered in sanscrit texts.
