The battle of Moyra Pass took place over a number of days in early October 1600, but there was in fact a standoff lasting from mid-September when Lord Mountjoy first established his camp at Faughart, until he gave up and pulled back to Dundalk on 9th October. On 13th October for reasons which are still not known but are thought to do with other events in Derry and Donegal, O'Neill pulled out of the Pass. Mountjoy marched through unopposed the following day, dismantled O'Neill's barricades, trenches and fortifications and began felling the woods and picking a site for a fort.
For a brief, popular account see this link:
For a more detailed account see attachment ‘Trench warfare in the Gap of the North, 1600’ from Cuisle na nGael (Newry, 1987)
For the really serious history anoraks, the PDF attachment below is believe it or not a 650-page Ph.D thesis from the Univerity of Rio de Janiero in 2005, which cites information I have not seen elsewhere. The main account of the battle begins on page 498