This is one of the best threads I’ve read on this site in a long time. Elk hunting is darned hard, especially if you are a flat lander with limited budget and vacation time. If I can add anything to this great thread without repeating a lot of the same points, I’d say you have to expect to see an elk, and keep at it with this expectation.
Just seeing an elk an elk is a huge win as a newbie. If you can find one, then you can kill one. The darn things will show up in the ‘wrong’ places and at the ‘wrong’ time. As KC stated “hunt all day” and I will add expect to see one at any time of the day.
On public land, I say forget sitting on the parks and openings. Concentrate on the travel areas around these spots. At first and last light I like to be slowly moving around grazing sites hoping to catch them up and moving and covering as much ground as I can. There’s so much area that the odds are slim of just sitting and having an elk come walking into an ambush. Also elk are much more forgiving of movement the deer. They smell you and you are screwed, but if you stay downwind you can work them and move with a herd to get a shot IF you can spot them.
