Script 1 is executed and the elevator ( just a floor and a ceiling ) rises to the second floor.
After that, scripts 2, 3 and 4 are simply not executed and the elevator will not budge.
Your lines are set to be triggered once only. So they get triggered when you leave the elevator, do nothing due to the lineside check and when you go back on they are no longer active. You need to set them to repeatable and clear the special explicitly in the script.
Setting the lines to repeatable did the trick, although I must admit that I don't understand why I had to do this.
Walking over the first linedef triggered script 1 to move the elevator to the second floor.
Leaving the elevator, the second linedef was crossed but did not trigger script 2 since I crossed it from the front.
Turning around and crossing the linedef from the back should have triggered script 2.
The 'action' that is triggered is the starting of the script, not the elevator move. Even when it does nothing the script is still started successfully and the line special cleared