Is there a cover on the drawbar that you can pull off and find a junction box underneath?
I don't know anything about 105's, but all the 101's have that, I've rewired several for 12v flat 4-wire connectors.
What I've found works nice is wire loom and black plumbing repair tape and bullet connectors.
If you don't have any already, you also can go to Walmart and pick up a couple bullet crimp connectors. They should fit the trailer junction plugs perfectly so you don't have to hack any trailer wiring, just plug in. You can also grab the wiring and trailer-side plug while there, and some wire loom to make it tidy. If you want to get really tidy about it, like I've started to, you can pick up a roll of the black rubber-like stretchable plumbing repair tape to wrap around the junctions and outside of the wire loom.
Crimp those connectors on to your 4-wire male wiring connector, then plug them in to the corresponding trailer wires according to the linked page in this thread. Wrap the loom around the wire, then wrap the plumbing tape around the loom in a few places and around the 4-wire connector, and you're good to go.
It doesn't have to be 4-wire flat, either, you can pick up whatever connector would work best for your tow vehicle. I just made one with a 7-wire RV plug so I can stop using an adapter for my regular trailer.
I tried to re-use the factory harness with the plug cut off and replaced with an RV plug, but I found that cable too heavy, it was a serious PITA to work with and not really purposeful.