Usually some calls to biologists are the first step, or others who spend time in your unit - wardens, other hunters, etc. Bios will know the seasonal patterns.
In CO they have maps on their website for every unit that show winter range, summer range, and the migration corridors. They make it so simple, even a caveman could do it.
In AZ/NM, the units I have hunted, there are definite early season areas and late season areas. I am not sure if that is due to weather/seasons, or due to hunting pressure. In the rim units, winter, if you have any, will push them lower. In your other areas, as soon as the shooting starts, they head for some of the terrible country that people don't want to go to.
There are also dry year and wet year areas in AZ/NM, causing movements and concentrations that will consistently have elk. It really comes down to the seasonal needs of the elk, with each month have different needs, and matching the area that fills the elk's needs to the time period you are hunting - pre-rut, rut, post-rut.
In MT, ID, WY, CO, and most the states with much winter, you will have definite patterns of movement, based on weather, that cause elk to leave their dispersed summer and transition ranges, to heavily congregated winter ranges.
Hopefully that gives some more ideas of what I look for. I am not the expert. Many guys here know a lot more about elk than I ever will. I think my hunts are very similar to the guy who draws a tag once every three or four years, most likely in an area far from home, requiring them to sort things out pretty quick, or as you said, count on luck. Luck is not always our friend, so I try to not rely on that option.
