Maybe mine tend to be the reverse of spot and stalk, more like stalk and spot.
I would hike a lot and most often would see elk close and usually see them about the same time they would see me. Close encounters. If real close I would shoot offhand. If a little further then I'd sit wherever I was. A few seconds sounds very brief but is plenty of time to sit and take careful aim. I carried an old BLR that is well balanced and handles well. What helped most was an M8 4x scope that has real fast target acquisition. 7mag.
These days I can't hike that much and I've had to adapt. I'm most likely to post someplace with my Sendero and wait, also a 7mag. I would not want to carry it many miles. Practice for me at the range now is a whole lot different than it was with the BLR.
