It might be as simple as buying a new T/S flasher. It sounds like the T/S handlebar switch is working if it is cycling the flasher when slected. The other electrical portion within the flasher that completes the circuit flow to the lights though may have been toasted.
"Time is the coin of your life. It is the only coin you have, and only you can determine how it will be spent. Be careful lest you let other people spend it for you." - Carl Sandburg