I think this is impossible but you can try to play around with the summon skill. If i got you right you are trying to set the summon time (time during pet is summoned) for the first pet to 10 secs? If someone summon his first pet it will disappear after 10 secs.
You can try if there is a param which will control the summon time. But i think the whole summon skill is hardcoded in the gs.
