Yes, there really was a rebellion of 1798. It was one of the few in which a unified Irish army fought against British troops. But being Irish, unified did not mean organized, and the rebellioin failed. It was in parts heroic and the memory of this rebellion was memorialized in the song "At the Rising of the Moon." This song was written sometime after our War Between the States as a unifying anthem for the Irish people. They just never stopped trying. The song does not refer to the actual moon, but to the symbolism of a full moon representing the four counties (quarters) of Ireland coming together. The reference to the full moon occurred, as I noted above, in a catechism from County Cork in 1797. This was not a minor skirmish but a major rebellion and should be known to anyone who is even "part Irish." It was certainly familiar to Genearl Hardee as he pondered over flags during the winter in Kentucky.
Re. the flags of the said rebellion: They were almost all green fields, some with gaelic slogans painted in gold, and some with Irish harps. The identity of this rebellion with the full moon came with the writing of its history.