There is a spring on the trail, but its not at the switchers. If that were a spring, it would not turn on and off so quickly in response to snowfall and melt. Its just surface runoff from the snowfield immediately above. It gives the appearance of a spring because it runs under the talus in places, giving the appearance of emerging from below grade.
The real spring is just below Outpost Camp and feeds the stream at the first crossing when entering Bighorn Park from the east. It is recognizable because it flows all out of proportion to winter snow and current pack/melt conditions, and its source looks like solid rock a little upstream of the crossing.