OK it sounds like the indicator stalk has gone then.
If the home safe lights are working and the side lights turn on when you open the car (welcome lights) then that shows there is no fault with the lamps themselves or the GEM.
The switch isn't expensive (if you're out of warranty) so don't panic.
They are really easy to fit (it's a Ford)
I would just reccomend that if you have a friend with another similar Fiesta (it doesn't matter if they haven't got a Fuel Computer) then see if they will let you borrow their stalk to try in yours.
If the problem goes away when you fit their stalk then you've solved it, if not then you need to look elsewhere for the problem but at least you haven't wasted money on a switch.
Hope this helps