The spelling of the phrase "gat on wagon" is somewhat unusual and may cause confusion for those unfamiliar with its pronunciation. The word "gat" is a shortened version of "get" and is pronounced /ɡɛt/. "On" is pronounced as it appears, /ɒn/, and "wagon" is pronounced with a soft "g" and "a" sound like "wag-un", /ˈwæɡən/. When combined, the phrase is pronounced /ɡɛt ɒn ˈwæɡən/ and means to join in or participate. It is important to note the unique spelling of this phrase when interpreting it in written communication.
I apologize, but it seems like "gat on wagon" does not exist as an established term or phrase in the English language. It might be a regional or slang term that is not widely recognized or documented. Consequently, it is not possible to provide a dictionary definition for this specific phrase.
If you have any other term or phrase that you would like me to define, I would be more than happy to assist you.