Best time for finding pheasants:

When I can, I go out when it is legal shooting time and stay until I get some. Here that usually means 9:00 a.m., but I also go out in the late afternoon, after work. To me, the " best time" is that afternoon after work time, because there are few hunters around and I can unwind from work. I think there is no " better" time of the day to hunt--if there are birds, the birds are there all day long.
As far as time of year, I think the opening weekend and following week is usually most productive/best, if the majority of the crops have been harvested, otherwise, it generally get better as the crops are harvested and the available cover diminishes.

Best surroundings:

Really the best place and time to hunt, around here, on public lands, is when the farmer in the field next to the public land harvests his corn. The birds move into the public cover. Whammo!!

Pheasants are found in grassy fields around here, mostly. CRP grasses, cattail sloughs, filter strips hold birds.

Using a .410:

Not a good idea in the hands of a novice hunter/marksman/wingshooter.