I have only called in a few reds, but they seem to be a whole lot smarter than grey foxes are. I think they like more open areas than greys do,(especially small farms with ducks and chickens) and they pay attention more to the wind also. Talk to local farmers and see if they are missing any chickens, if so, they will probably be happy for you to take care of his problem.watch for them to circle especially if they can get downwind. They seem to really like the sound of distressed chickens, but most anything will probably work. I'm no expert, but this I have learned from past experiences. Red foxes are few and far between here( South Boston VA),and all anybody really sees are greys. good luck. hope this helps.
P.S. as for the best time to call I really don't know. Personally I like the early morning, but you may experience someting different. These guys on here know alot more than I do, so mabye than can help you more