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Diagnosis
My Check Engine Light (CEL) came on, so I took it to Autozone to get a free reading of the code (most auto parts shops will do this for you).
P2647 - Rocker Arm Oil Pressure Switch (VTEC Oil Pressure Switch) High Voltage
The car was driving fine if you stay below 2,500 or 3,000 RPM, but if you start quickly or need more power, the car would shudder and basically not respond until it got back down to lower RPMs.
Parts
I read through this forum and watched a few Youtube videos and decided that it was likely the actual switch that was faulty (part #12 in the diagrams you see in this forum). You can search for "Honda 37250-PNE-G01" and find a lot of places to buy them - Ebay, Amazon, H and A Accessories, etc. I wanted to get my Element fixed as soon as possible, and Autozone actually had one in stock at a nearby store, so I picked it up.
Process
After reading here and watching a couple videos, I saw that removal and installation was pretty easy (though hard to see). You have to reach in the back left, behind the back left side of the engine. You'll see the power steering hose right here, attached with a clamp to the engine. You can unscrew this pretty easily (10mm socket, I believe), and pull it out of the way a bit to get a better look at what you're doing.
In the back, you have a little metal box with an open top (part #6 in the diagram). On the top of it, you have two circular connectors sticking up. The one on the left is...well, I don't know...but the one on the right is the oil pressure VTEC switch. Both of these are just electrical connectors, so you can feel around to push in the on the sides a bit to release them and then pull them up. Once you have unclipped them, you can get go the sensor. This requires a 22mm socket, but it must have a deep head because the sensor is about 1 inch long, so a normal socket won't fit over that to get to the base. Once you have the right tool, you can simply unscrew it and pull it out.
Note that there is a tiny little black o-ring in there. My new piece came with a new o-ring, so I replaced it, and most people would recommend replacing it if you already have the piece out. (It's a cheap little plastic ring, nothing more) So I just put the new o-ring and sensor in, tightened it up, put the connectors back together and then clamped the power steering hose back on.
All in all, the work just took about 15 minutes, IF you have the right tools. I drove the car around for a while, testing it out with quick acceleration (well...relatively quick, considering this is still a 4 cylinder Element, after all) and pushing it where the VTEC would normally kick in. The car responded well, and I drove a bit on the freeway at 65-75 mph to test it out, and I had no issues. About 18 hrs later, after the car had gone through a few cycles of turning off and on and the VTEC kicking in, the CEL went off, so it seems like the problem is fixed!
[Note - many people also recommend taking out the whole unit and replacing or cleaning the screen. That's a good idea, and I'll probably replace that soon, since it's fairly simple to do.]
Likely Cause
The car had been sitting for a while after a long roadtrip, and I was a bit overdue on an oil change anyway (maybe 1,000 miles over). In addition, I have a minor oil leak, so with all those combined, I'm sure my oil was pretty low and probably a bit gunky. I can't be sure, but based on comments from others, I wouldn't be surprised if that was the main cause of this failure.
Summary
Parts/Tools - 37250-PNE-G01 sensor, o-ring, 10mm socket, DEEP 22mm socket (DEEP 7/8 in socket also works)
Cost - I bought the sensor and o-ring for about $70 total. You can get one for about $20 online if you are willing to wait for shipping (sometimes from China), or you can buy the OEM ones online for $55-70 (and have to wait for shipping)
Time - 15 mins of actual work, plus I spent about 1.5 hrs reading this forum and .5 hrs watching Youtube videos
Thank you to everyone who posted here, as you saved me a LOT of time and money, so I wanted to also pass along my experience for others.