While diksha mantras can be seen as Guru, there are certainly manifestations which have closer connections with the Guru tattva, and both initiates and non-initiates may benefit greatly from doing certain works during this period. Shiva is Adi-Guru so any work involving Mahadeva would be good, and Krishna also acted as Guru and can be propitiated. Mantras for Veda Vyasa are very auspicious during Guru Puja, and this can be combined with Mritunjaya to make it more powerful. For those who don't have a personal Guru or mantra, then the Guru Gita would be great to either chant or listen to during the eclipse period. There are no limits to what one can do with sincerity and an open heart, so to all the great Beings of all times and those who have inspired you, do make a heart call and ask for their blessings. For those who practice or admire teaching from the Buddhist tradition, one can do the mantra of Padmasambhava during this eclipse, and the prayer of Samantabhadra is especially powerful during eclipse (it is stated that if one sits as Samantabhadra and reads this prayer aloud, then anyone who even hears it will be liberated within seven lifetimes). In terms of planetary sadhanas, the best choices for this eclipse would be Brihispati, Shukra, and/or Surya.
For those sadhaks who intend to sit chakra, for longer eclipses, it is best to sit the chakra at the end period of eclipse and for shorter eclipse, it's best to sit immediated after. This eclipse is short, so best to do sadhana during and then sit a chakra after to seal it.