Start with the logic_timer disabled (I assume you have it refire every 5 seconds non-randomly). Have the timer fire the tf_point_weapon_mimic on its OnTimer output. Have the trigger brush enable the logic_timer when someone enters it (if you use the OnStartTouchAll the timer will only be enabled when someone has entered the trigger brush if there was no one in it at that point. Give the trigger brush this output as well: OnEndTouchAll (when the last person left in the trigger brush leaves this will fire, so as to not disable the timer when anyone leaves at any time) , disable (NOT KILL) the logic_timer.
EDIT: You edited your post after I answered your original question. Although I have an unorthodox solution to your other problem. I'll get back to you when I have a look at an old vmf. Please note however that if you have in mind the type of "homing in" that is featured in Pyro Dodgeball then I'm not sure how to do it. My method simply aims the tf_point_weapon_mimic at an object, fires, and forgets.