Sorry Scoot, but there's no such thing as a traffic pattern at JC! There are so many ways to approach it that the word just doesn't apply.
There are however, some things that can help visualize what has to be done to make a nice no sweat landing there. If you use normal pattern altitudes of about 800, 600, and 300 for JC you are going to be
way down in the canyon and had better be comfortable with flying 5 kts above your final approach speed while your right wingtip is 20-30 feet from the rocks. For me, that's no faster than 65 knots with 20 degrees flaps. It's also a VERY tight pattern that really is just a 180 on to final, and requires pretty much idle power from crosswind over the South end at about 1000 AGL. On downwind you are only about 800 feet from centerline. Try that at home a few times, it's about 1/3 the size of most folks patterns.
Cubs, Scouts, 140's, anything that can fly comfortably at less that 60 mph can do this with no problem. It's harder in a loaded 185 doing 75 kts.
What most people do is to fly over at 1000 to 1200, announce, then fly three miles North in the middle of the canyon and turn around near Yellowpine where the East Fork comes in and there's at least a mile of turning space at 800 AGL (5800 MSL). You are out of sight of the runway there, so just set up a 400 fpm descent at 65 mph until you come around the corner and can see the runway at about a mile out. Then you can judge your final descent and check for people and planes on the runway. Almost everybody ends up too high and too fast and has to slip it in or go-around the first few times in there. It is 3400 feet long so a midfield touchdown is really no problem, but it sure LOOKS small the first time. Check out the picture on Airnav.com. If it looks like that on short final you're WAY too high! Almost all landings are on 17, it takes about 15 knots of North wind before a 35 landing makes sense and nobody without lots of backcountry experience should be flying around in canyons with that much wind anyway.
It gets kinda crowded some weekends and folks do like to come out and kibitz or take pictures, so don't expect to see a completely clear runway. It is 150 feet wide, though, and we've never had anyone run over yet, so just use your landing light and land.

Go-arounds below about 100 agl at the threshold can be interesting in anything with less power than a SuperCub, 180, or Scout type. If you have to go-around, jog left to get over the creek for more room.
It may look intimidating from 8000 on the way in, but all our canyon strips look that way, and JC is actually one of the largest and safest.
The key is to get way slowed up way early and get right down in the canyon. Most of us could do a 360 at 300 agl right over the airport if we used the canyon turn technique discussed earlier on BCP. It just doesn't look like it. Don't try that on a windy 90 degree afternoon though!
JC has the justly deserved reputation as the top backcountry strip in Idaho, if you call hot showers, toilets, fire pits, and acres of irrigated grass backcountry.
So come on out!
Rocky