I know exactly what it is since I just had the same problem. It's the silicone in the LED strip basically melting in the heat. I first thought it was tree sap dripping down the side of the coach but had not been under any major trees. I looked at the awning and sure enough it looked just like yours.
I removed the LED strip and cleaned out the sticky mess with a light scraping and Acetone. I ordered a new LED strip from Amazon that fit perfectly in the the narrow slit, changing to warm white LEDs which I like better than the cool white it came with. You will have to change out the plug on the end of the strip but that's all. Here's a link to what I ordered for less than $20 with tax. Carefree wants $80 for replacement LEDs.