If the blinker doesn't flash when you indicate on either side you sound right to be guessing that the flasher unit has gone. This is a generic item that is common to all cars, you should be able to get a replacement at your local car parts store. If you can remove the under dash panels, find the flasher unit and plug a new one in you can do this job yourself.
In my experience, where the flasher unit is usually depends on who did your conversion.