I don't think you can get a source earlier than Caesar.
Now, regarding "Gallo" and "Gullo" ~ most pre-French latin based languages/dialects in what is now French were called "Gallo". "Gullo" is sometimes found in Sicily and is a different word.
Now, about Celtic clan names in what is now France back in Caesar's day ~ they reached off South across the Mountains into Northern Spain. The dominant Celtic group in what is today's Galicia (including Northern Portugal) had come from the Danube around 1000 BC. They had taken over a large chunk of the North Coast held by the Basque. In 700 BC whereupon they invaded Ireland (and Britain). This is the reason the Irish spoke a Celtic language until recent times but are otherwise clearly genetically identical to the Basque.
It would be highly unlikely for "Galli" to have failed to appear in Spain some time in that history. In fact, Hannibal's ally in Spain during the Punic wars was a fellow named Magolis, or, as we'd put that today Mac Wallace, or McGallis.
Do not let modern spelling conventions blind you to the reality of the past.
Now, give me an Italian reference older than Hannibal, the Greek historians, and the Milesians!
Now I’m completely lost. Are you saying everyone is Irish? ;-)
Just kidding. On the question of ancestry, the furthest I take it back is to the country from where the person’s ancesters emigrated to the U.S. That’s why I consider Galli an Italian name.
You’ve definitely traced it back much further than I did. :-)