I know next to nothing about motorbikes. (I find it challenging to separate a Vespa from a Norton, which is about as recent as my vague knowledge gets!). However basic electrical theory indicates that, if there's a buzzing sound, there must be some powerto the circuit, so that rules out a fuse problem. That really only leaves one component which could fail, affecting both indicators simultaneously, i.e. the flasher relay:
http://www.wemoto.com...picture/Flasher_Relay
Chris