I also do the exact same thing.

 

I have owned 2 bikes with self-canceling signals. Both were Yamahas from the late 70s or early 80s: an XS650 & XS750. I understand many other Yamahas from the same era also had them.
The system was controlled by a little electrical module mounted under the seat. If you have access to a motorcycle wrecking yard, I am sure you could find one for cheap and adapt it to the KLX without too much trouble (?).

 

My first bike that I bought new myself was a Honda NX250. Leaveing the turn signals on bugged me so much that I worked out how to build a self cancling device that worked on inertia for the turn backed up by a timer. Then I went into the delaership to buy some oil filters and overheard a salesman talking about how the bike he was showing had self cancling turn signals. I was so bummed I thought I had invented the latest greatest thing for motorcycles. That was the first of several things I was the "Second Inventor" of.
Cheers, Jim