From the stated facts in this thread , this is how I feel about it :
Zimmerman was well-known by his neighbours to be doing this . They had no issue with it that I have heard , and encouraged him to do so .
He was well-known by the police to be doing this as well , who encouraged it as well .
He was , after the phone call was initiated , apparently asked to keep a close eye on Martin .

To this point he was right in all he did .

It was suggested , as would be the norm , that he leave it to the police from there , however , he acted to keep the suspect in sight , which was the former instruction .

It's hard to know , given that I have no idea what the actual terrain in the specific area was , but the suggestion here seems to be that the act of disappearing from sight was a suspect move in itself .

They found nearby , not right at the scene , burglary tools , which more than suggests that not only was Zimmerman right about this young man being suspicious , but that the young man had ditched the tools and gone back to deal with his pursuer so as not to be caught "red-handed" with them .

At this point we need to remember that Zimmerman had a gun .
He had not drawn it , walking into what had to have been , effectively , an ambush .
Though likely pretty high on the adrenaline of keeping the "perp" in view , with senses on overload , he hadn't walked in ablazing .
He expected him , clearly , to try to flee .

He didn't , and the two began to fight .

Leaving stashed the burglary tools says that Martin either didn't think that Zimmerman had a gun (going back at all unarmed says that , too) , that he wanted to either appear innocent upon their meeting , or not be open to greater charges in the end by using a weapon for the beating .
And , we mustn't forget Martin's state of mind , either , full of adrenaline as well as a wash of teenaged hormones , having just decided to stash his tools , and guilty of being suspicious .

There does not seem to have been any discussion , as the concealed weapon would have appeared before it did .
Thus , a sort of ambush is more likely .

It seems pretty likely that the gun , itself , emboldened Zimmerman to leave his car , but as it only appeared after the two were on the ground , it doesn't suggest he was trying to apprehend anyone , but rather that he was trying , as instructed , to keep him in sight .

It doesn't really make sense that when you are beating on someone , you stop to shoot them as well .

But it does make sense that you'd shoot someone if they were beating on you .