No actual answer yet, but I have the information on that word filed around here somewhere.
The best that can be said, before saying anything else, is that like many words connected to tarot, its origin is uncertain. It must have multiple origins, and people picked it up and assimilated it to whatever other words in their language sounded like it.
In one direction you have it becoming Bagatello/Bagatella=Bagatelle - something of little worth (since it is the number 1); on the other, it goes to Bateleur as well, a guy who does magic tricks and acrobatics.
Kaplan (vol. I, p. 16 French edition) lists English sources as having the form Pagad or Pagat; and also the widest variety of names in general.
For Italian he gives Bagatino, Bagatto, Bagattel, Bagat, Bagotti, Bigatto.
French only has Bateleur or "Jouer de Gobelets" (I've never seen that on a card).
So perhaps the obscurity of the word give rise to different assimilations with known words. Or sometimes just its own word, which means nothing more than "the first and lowest trump."
But in Bologna, the card is called "Bégato", and I read that it means "Baghdadi", since the "wandering gamesters" were presumed to come from there.
see:
http://utenti.lycos.it/taroccobolognese/cap1.htm
"Bégato: the Italianized transliteration of the name Bàgatto, in the Bolognese dialect (Béghet). The word Bàgatto probably derives from Baghdad, the city from which came, or were presumed to have come, the itinerant gamesters. The attribution is in any case uncertain."
"Bégato:
è la traslitterazione italianizzata del nome Bàgatto, dal dialetto Bolognese (Béghet). L'etimo Bàgatto probabilmente deriva da Baghdad, città dalla quale provenivano, o si presumeva provenissero, i giocolieri ambulanti. L'attribuzione è comunque incerta."
Ross
