Route 4 no longer connects to Sylvan Lake Trail (the route 4 loop was split last year, 2005, into two, one-way, spurs.) This is posted at the trailhead; however, looking at the trailhead map (not a topo) a 'reasonable' person would assume a simple bushwack (1/8 mile or less) would lead North into Sylvan Lake Trail. IT DOESN'T.
In actuality the spur was intentionally diverted to the east where it terminates and a large; heavily wooded ravine would need to be crossed to reach the Sylvan Lake Trail to Mt. Harney (difficult, though not impossible.) The actual (old) trail is heavily obscured by the rangers and about 400 chords of wood are 'scattered' on it to discourage anyone attempting to hike it.
If you must, it is about 1000' from the terminus and runs West to the edge of the ravine before crossing. However why? Clearly erosion control is in place and it only adds about a 1/2 hour to do both one ways spurs and see some awesome rock formation while in the Black Hills. Any serious climber could do both routes and Mt. Harney (round trip) in 4 hours.
I highly recommend doing Cathedral Spires first; doubling back (via car) about 3 miles to the Sylvan Lake (route 4) trail and doing Mt. Harney.