The electrical configuration you described is teh most commonly used - where a switch turns the lights on and off. Our wiring harness comes with a surface mount switch that does just that. The harness can be made to come on and off with the headlight, but that requires additional wiring.
The standard set up you want is simple. Red wire to battery positive. Black wire to battery negative. White wire to a s witched source. Since you are planning on wiring in a brake light module you may want to use the positive going to the running light (not brake light) as your switched source. However there are other equally do-able choices for a switched source depending on model of V-Strom.
The wiring instructions for the LED frames depend on model chosen and come with the product. The one you selected is simple. Red wire to brake postive lead, White wire to running light positive lead, black wire to battery ground. Don't ground to the frame on a V-Strom, go straight to the battery or the negative return in the wiring harness.
Feel free to call me as sometimes these things are best discussed on the phone, but the installation you have selected is pretty simple. 509-539-2288