When I bought my first 2012 Zero, the turn indicators didn't work at all, even before I left the showroom. The dealer then removed the turn indicator flasher device from a 2011 Zero and installed that on my 2012> That solved the problem. That solid-state switch was located under the "tank" behind the headlight, as I recall. However, I am not sure where it is located on the later bikes. But it should be easy to find by tracing the wires from one of the flasher assembles or the turn signal switch. You might have to replace the flasher component if that is the problem. But first try spraying WD40, or something similar, into your bar-mounted switch.
If you do need a new flasher box, I believe that just about any one will work from a Japanese motorcycle, purchased from a local shop, or you can source one from Zero, which might take a while to arrive. I am pretty sure they don't cost much.