Tx: Landlord Posted 3-day Notice To Quit Expiring Late Friday Night, And Court Opens Monday Morning. When Should I Leave By In Order To Avoid "an Eviction" On My Record?

Location: Brazoria County, TX.
Landlord posted to the door a proper 3-day Notice to Quit at 7:40pm Tuesday night. 3 days (72 hours) from then is 7:40pm Friday. Court closes at 5pm Friday, and opens again 8am Monday.

I'm really busy with work to make enough money to survive, so I just want to understand my options for a hard "leave by" date/time while seeking to avoid the kind of 'eviction record' that would complicate future renting:

-Obviously if I leave before 7:40pm Friday, there's no lingering 'eviction on my record.'
-What if I leave by Sunday evening, before court opens on Monday, and email him pictures of proof? Would he still be able to file for an eviction hearing because I didn't leave by 7:40pm Friday? Would that filing follow me on my record? In general, can people "file" cases electronically over the weekend in Justice Court?
-Suppose I haven't left by Monday morning, and he files in court on Monday, and a trial(/hearing?) date is set for Thursday. If I leave on say Wednesday (and provide proof), show up in Justice Court on Thursday and present such proof to the judge, and the case is dismissed, would that be likely to be considered 'an eviction on my record'?

(I'm aware there could be further issues like suits for back rent or property damage etc. Ignore those concerns for now. I don't intend to contest an eviction in court, because at present my best understanding is that I have no legal defense, though I may look into it further. Ignore those concerns for now as well.)

Thank you in advance.