The original factory kit had an adapter and wiring that just plugged in to ready installed plugs. It got the power for the trailer lights from a wire already in the wiring harness. You can't easily find those specially made kits any more.
The universal "splice-in" kits require you to find the wires and "splice" them in to the wiring. It's probably easier for your case than the original kit because you can reach the wires you need without needing to take off the interior panels. The adaptor controls the trailer lights and it gets power from a wire you run up to the front inside or outside the body. I remember a message on this board from someone who connected that one to the rear power plug. (You have a DX so I suspect that's not an option.)
There are two kinds of "splice-in" kits. One just adds the trailer lights on to the same circuit as vehicle lights. The other one, the "powered" or "self-powered" version, runs a wire to the battery so the trailer lights are powered separately.
You NEED the self-powered version for two reasons. One, the most important, is that the tail lights are wired barely well enough to work properly. The wiring is as small as Honda thought they could get away with - and unfortunately for owners of the 2005-06 models, this wiring was too small for even the original purpose. If you try to piggyback extra lights, you stand a chance of burning out the entire circuit and it's expensive to fix, assuming you can still get the parts AND you can figure out where the damage is. I don't know where the fault was but it spanned several models, not just the Element. My 2005 Pilot had the same issue which is how I first heard about it. The "self-powered" adapters don't put any extra load on the original tail light circuit.
The other reason covers EVERY model of Element. Trailer wiring is the scariest wiring there is for developing short circuits, open grounds, gremlins - you name it. Without a self powered adapter, any damage from a short circuit ends up under the dash in very expensive places. You need that insulation from disaster.
How to tell if an adapter is self powered? It'll say "powered" or "self powered" in the description. It'll have an extra wire, probably red or green, and very long and coiled up that you run up to the battery under the hood. It'll most likely have little blue wire splices to hook it to the vehicle wiring which, while easy to use, aren't the best thing to use if they're exposed to the weather. Solder and tape are best but I have a feeling that's beyond your current skill level.
Sources? Online, you can get good deals from Ebay or Amazon, although don't trust ANY of Amazon's recommended "this is what you need" suggestions because they'll recommend anything based on single keywords instead of ALL the keywords. A place like etrailer.com will have it all. Carid.com has one. Check out this link to see a good example plus installation instructions.
https://www.carid.com/curt/tail-light-converter-mpn-56146.html?singleid=940122952&url=3622573
