I had a similar problem with my headlight washers ... It turned out that I just needed to re-fill the washer reservoir ...
I'd give that a go before you do anything else ...
first port of call.sorted mine when this happened
if i am correct the fog light has to be in the middle or to the right.
i d go with the idea of wiring in to the o/s/r reverse light,replace with rear bulb and sort a switch.