When I was down there last summer my friend and camped in 2 lacations. First one was right off the tail end of Engineer pass about 2 miles from Lake city, the second spot we found was as we were coming over Corkscrew pass towards the end of the trail on the highway 550 side there is a fork in the trail. Left goes past a mine the right side goes goes a back way between trees and meets back up with the trail dunping down in a staging area that has a small camping area to the right of it. If you go rightbat that fork you will find a small secluded camp site the would fit about 3 rigs maybe 4. We stayed there 2 nights. (Note; at the fork in the road there seemed to be a rather large area that could be used at a camp site for a large group, but it seemed that water drainage could be an issue if it rained hard enough). The site was about a 20 minute drive from Ouray which was perfect.
Corksrcew gulch Big site- 37.9235392, -107.6753400
Corkscrew gulch Small site - 37.9240909, -107.6749085
Engineer pass Small site- 38.0208869, -107.3860145 (this might not be exact but it is near these cordinates)