Tincup Pass wouldn't make that much difference on the west side, you still have to get out of Taylor Park. On the east side it would have come out in the vicinity of St. Elmo.
If I remember correctly, the west side of the pass isn't all that steep that would warrant a tunnel, however on the east side there is an adit to the south of the jeep road at the 12,000 ft level. Maybe that is what was found. I don't know of any adits on the west side.
There is an outside possibility that the goal would have bee the Tincup area and the miens up towards Cumberland Pass. Looking at a topo map you can see some plausible routes.