Let's try the hypothetical again, only this time let's have the judgment be signed Thursday, January 3. The first day to count would be Friday, January 4 and the 30th day would now be Saturday, February 2, 2019. Since the 30th day is now a Saturday, the period does not end but would go on to the next day which would be Sunday, February 3, 2019, which does not end the period and the deadline is moved yet one more day to Monday, February 4, 2019. Again, barring a technical efiling problem, the notice would be late on or after midnight Tuesday, February 5, 2019.
For a third time, the judgment is signed in Montgomery County on Thursday, January 17, 2019. The first day is Friday, January 19, 2019. The 30th day is Saturday, February 16, 2019- no good. The next day Sunday the 17th is no better. In this case, though, Monday the 18th is President's Day, a holiday in Jefferson County where the appropriate court of appeals sits, Beaumont's Ninth Court of Appeals. So it is no good either and the last day for filing the notice of appeal is Tuesday, February 19, 2019. Efiling willing, the notice would be late Wednesday, February 20, 2019, at or after midnight. Texas state appeals courts are pretty good about announcing their holidays. If the appellate court has not indicated on its web page whether or not a day is a holiday a good practical rule is that courts of appeals follow the holidays of the county in which they usually sit, and the highest state courts follow the state government holiday schedule. Parties with their backs against the wall may try to get, say, a state holiday counted when an appeals court was open. I shudder to think what would happen if the holidays of Nueces County, one home of the Thirteenth Court of Appeals, did not match with the holidays of Hidalgo County, the other home of the Thirteenth. Those are the nightmares of appellate nerds.