Arduino as a switch

I have an Patlite PEW LED lite that is run by USB. What I am trying to do is control the LED from Arduino. I need some help to figure out if I can power the entire thing from the Arduino. If not, I can plug the light into USB to power, but then turn on the light using the arduino.
I got this image from the spec sheet.

Need help trying to figure out how to write a sketch to complete the red line and yellow line without supplying power from arduino. When I just connect the red line, the LED lights up without any other wire connected. Just confused as to where to even start. Thanks for any help.

"confused as to where to even start"
Us too. How about a link to a spec on the part?
For example, what is the deal with the Gray/Black line and the 120/230V ground line?

Here is a link to the light I have.

http://www.patlite.com/product/detail0000000064.html

Except this was purchased from Germany and has the addition of a USB controller. I found a program that can control the light via USB, but want to control it from my arduino. I took a picture of the USB controller that is in it already.

I looked up what the SIM1-0524 module is and here is the sheet for that.

Here is an image of the top portion of the light.

The gray and black wire I believe are the power. If I plug it into a USB port, I can turn the solid LED light on by combining the yellow and red wire. To have the flashing light, I can touch the yellow and brown wire together. Seems easy to write something up, but it never is. Thanks.

Per Fig 2 on one of the pages, looks like all you need to as a ULN2003 to make the transistor contacts, your arduino can drive that.

Thanks for your help. Can't the arduino power the device also? I thought USB outputs 5v like the arduino?

Found out that this is the PEW-100 (Rated voltage = 100V AC)

One thing the manual doesn't seem to mention is the isolation between the signal lines and the power lines - therefore I'd assume there is no isolation and that the signal lines can become live - in other words use opto-isolation or relays if you want to guarantee you and your Arduino's safety.