The following can be recognised as a "staff opinion", it has been reviewed and approved by staff leads.
I'll do my best to try and give a concise explanation of "Keeping eyes" though as ever,
no two situations are the same.
Example A:
Setting the scene...
Jim, Jamie and John are in the process of processing copper and are spotted by a single rebel who intends to rob them of every last ingot! The rebel threatens the group, Jim, Jamie & John decide to take matters into their own hands and after providing high quality roleplay, pull out their trusty rook pistols and engage on the rebel, missing every shot. The rebel reacts quickly and manages to take down Jim & Jamie. John however, was smart! As he saw his two companions drop to the floor, he made up his mind to attempt a swift getaway on foot, in search of a hiding place...
In this example, lets assume that the rebel has maintained visual.
Simply put, there is no exact timeframe that the rebel would have to fire upon John, it's all a matter of common sense. If the pursuit has been going on long enough for John to doubt the rebels intentions to fire upon him, then further roleplay would be requires in order to engage upon John. It should be emphasised that this is a roleplay server, if you're in doubt then you're much better off making an attempt to engage in roleplay first.
Example B:
Setting the scene...
Police have sighted a group of rebels with firearms at Agios bank. As soon as the police approach the bank the rebels decide it's time to leave and start to run off. One of the rebels is left behind in a dust cloud as the other rebels all speed off in their vehicles. The police manage to shout to the remaining rebel, demanding that he stops or would otherwise be "met with appropriate force", the rebel shouts back at the police telling them to fuck off and continues to flee down the road. At this point, the police have deployed a high altitude helicopter equipped with a thermal imaging camera and the rebel is in sight. The police get themselves back to their own vehicles and arrange an ambush ahead of the suspect that is still being watched by the helicopter.
Again, assuming that the police haven't lost sight of the rebel throughout and continue to maintain visual by means of the thermal imaging camera on the police helicopter. The rebel is not aware that the police helicopter has visual.
Should the police then engage on the rebel who has fled? That depends. If the rebel has no reason to believe that he's being perused and has reasonable belief that he had escaped the police then no. Again, this is a roleplay server, the police should be able to effectively ambush their target, engaging in RP before deploying any "force".
TLR, common sense prevails. If you're not sure, then you're always going to be better off providing the high quality RP before engaging in any hostilities.