I recently discovered this unnamed connector trail running from Webb Canyon straight up the hill to New Almaden. There are a few of these "straight up" trails near the Webb Canyon entrance, but for this one you'll have to follow the paved road until it dead-ends at the water tanks. Look to your right and you'll see the trail running uphill along the fence. According to the official park map, this area is fully within the park boundaries, and there are no signs saying you can't go there, so I went there! It's steep, warranting the T2.5 rating, but it's not that difficult, and there are some beautiful views along the way. (Note that you can avoid the steeper terrain by making this cache a detour from New Almaden.)
You're looking for a small Snaplock-type container with custom camo. The title should be a good hint. There's evidence of dried-up poison oak in the general area (as there is everywhere in Almaden Quicksilver) but it's easily avoidable by the most direct route to the coordinates.
Almaden Quicksilver trail hours are sunrise to sunset. Park hours are 8:00am to sunset. Happy hunting!