One of the winter projects for my Uly was installing 1125CR mirror/signal lights. A 4-wire trailer adapter (separate tail/signal to combined tail/signal) provides running light functionality in a simple and tidy fashion:
I didn't want to snip into the stock wiring, so I soldered appropriate bullet connectors to the trailer adapter wires. The CR mirror wires were extended with pigtails. The module is zip-tied to the cross brace under the flyscreen.
They are nice and bright, and will hopefully add some conspicuity. We shall see how these LEDs hold up at 100% duty -- with luck, their brightness and/or life won't be diminished.
I recommend paying a little more for a good quality (i.e.: brand name) adapter that states it will work with LED lamps. I started out with a cheap one, and I had hacked the wires off of it before I discovered it was either defective or not functional with LED lamps. Should've tested it first
I also recommend using a blob of dielectric grease in all connections to keep moisture out.