Although a spritz of contact cleaner will likely solve the immediate problem (not being able to cancel the signal), the inside of the switch mechanism does need to be lubricated after it is cleaned, because there are quite a few mechanical bits in there.
It's not difficult to take the left handlebar switch assembly apart for a thorough cleaning and lubrication. Just take a lot of photos as you disassemble it, because the process for re-assembling it is not intuitive, and the various wires and clips within the assembly need to be put back in exactly the same positions that you found them in.
After taking the turn signal switch apart and cleaning it, I used dielectric grease to lubricate the moving parts of the switch assembly. It now operates much more easily (in other words, with much less effort required) than it did before.
Michael