If you climb Timp at night you won't really see that view on your way up. You might catch a glimpse of it as you make your way down, but if you are like most people you will be looking at the trail, trying not to trip on rocks and feeling the fatigue that befalls those who climb mountains.
Another tip would be to climb during the spring. Sometimes the snow can be a pain, but the mountain is so green. When I climbed it for the first time we saw a girl hiking along the trail. In front of her, two mountain goats walked along as if they were her pets. It's not uncommon to see these animals on the mountain. There are quite a number of them.
Mountain goats are humbling creatures. They live in the mountains and must wonder, what in the world we are doing up there. We aren't normally scavenging for food or getting away from predators, unless you call sedentary life a predator.... What would draw us up so high? Most of us are pretty inept as compared to them. As good as we get at navigating the terrain, most of us won't come close to what they can do. Of course we can rock climb and use our hands to scale things they wouldn't dare, but if most anyone tried to keep up with them in their element, they would leave them in the dust. The only hope some might have would be to out-distance them and even then it might take a while.