Traditional trigger means that you have to press a button to make the elevator move. Actually, it's this very trigger that launches the script. The trigger does nothing else. Yes, indeed, in Radiant the trigger is in no way connected to the func_static you use as an elevator. Well, it may alter the appearence of the func_static.
The trigger contains a trigger_multiple (if use want to surf with the elevator up and down, up and down, up and down... pardon me, got stuck like a bad script).
The triggers you make by drawing an ordinary brush, with fitting proportions in a suitable place (near the elevator). Then you select that brush and press right mouse button and select from the pop-up trigger_multiple. For convenience, texture the trigger with trigger textures in the system texture group.
But you can also place the trigger on top of you elevator with no switches, so that the elevator lauches automatically, when the poor fellow steps on it.