Inquiry: BAGATTO

For those who do not know, the bagatto is the lowest of the 21 (or
25) tarot cards. (Don't be concerned with "taro" and its fake
etymology; there is historical evidence that it is one of at least 2
French words which tried to express the Italian "tarocchi." I have
already sufficiently derived the historical meaning of this word.)

Now, BAGATTO is an obsolete Italian word, used as the name of the
figure on the lowest tarot card (14th-15th century). A dialect form
of it, in northern Italy, is BAGAT. Later it was translated in other
languages as the "magician." The earliest or 15th century extant
(Italian) cards portray the BAGATTO as a magician (prestidigitator),
with either dies or shells on a small table in front of him. (Forget
about all the esoteric meanings of the 18th century and the
divination practices in that century by Gypsies.) I have some clue
from at least three languagues about this uncommon Italian word. It
is unknown in Latin; if it existed, it would be "bagactus" (as CT
normally became TT).
Thus, these are the forms to be considered: BAGACT and BAGAT.
Any suggestion from your linguistic knapsack?