Is the trailer light on the dash not working ? it should flash once every time you indicate. and if you have a trailer fitted will continue to flash when indicating.
this is controlled by the flasher relay (think it has 5 pins instead of 4) the extra pin powers the dash light when extra current is drawn.
if the trailer is fitted with LED lighting this may not draw enough extra current despite the indicators working on the trailer you wont get the dash light and buzzer may have similar symptoms with led.
the relays are cheap and simple enough to replace just plug and play.
personally i like the light not an annoying buzzer