If the OEM turn signal has only a ground and hot, you won't get running lights without running another wire from your harness that comes on with running lights. Unless I don't understand the diode situation, which I don't
The resistor is used simply to generate enough of a draw to activate the electro mechanical switch in your blinker module. Easier to just replace that module with one specifically designed for LEDs. I have one on both my bikes and it's literally plug n play. If you do that you don't need the resistor which is a bad solution to the problem. Since I don't know what kind of bike you have can't give any actual products but if you google LED blinker relay (your bike) you should come up with one. I got one online and the other at cycle gear.
So if you run a running light wire from your harness to the lead on your LED for running lights, hook the flashing lead for each side up to the signal prong on the LED and buy a LED flasher relay, the wiring is much more simple.
I have no experience with your bike so if any of this doesn't apply to BMWs can't help ya.