OWAP, there is no set answer to your question. You have to take what hours you are allowed to fly and attempt to use it on the incidents where you can be of most use. You have to use your experiance to know which to ones they would be.
You will never satisfy the ground guys all the time. I fly five to six hours a shift and still get the ground guys complaining that we are not available. Or that there is not another ship to help, or why should you have time to eat, or leave when it is a mess on the ground just because you do not have any fuel on board and no second ship to relieve you. The list goes on and on.
Remember, it may be a "token gesture" to the ground guys, but the crooks see it as one reason not to do anything in that area as it will be more difficult to get away. Showing the "flag" has a lot of psycological effect on them.