Am I on a known, mapped trail? If so, take a bearing on the elevator, transfer the bearing to a line on the map (allowing for declination), and you're where the trail and the bearing intersect. (Assumes that the trail does not double back on itself, so that there would not be more than one intersection.) This seems too easy a solution, since it's just a variant of triangulation, with the trail itself serving as a landmark, which violates the conditions of the problem.

If I'm not located on another map feature (road, trail, creek, etc.), I'll need to think a bit more.