I'm making a leap of faith here that perhaps after Gibson's battalion of mounted rifles was dismounted in Sept., 1862, that it then became part [or perhaps the essence] of Hawthorne's [later Chew's] battalion. Which, of course, was subsequently consolidated with Hawthorne's regiment.

This "leap" stems from the loose connection of Tumlinson's company, which seems to have commonality with all of these units.