I have no experience of a jazz washer pump, but it may be similar to a couple of cars I have had. These had a filter in the bottom of the washer bottle protecting the pump, but even so the pump can get clogged with gunge which could jamb the pump. As others have said all sorts of nasties can grow in there unless you maintain a good concentration of screen wash additive, even in summer. I once bought a 2 year old used car where the washer fluid was like chicken soup with long tendrils of seaweed growing in it.
Also on many cars the rear washer uses the same pump, but running backwards ,with one way valves. Not sure about the jazz. But its worth checking to see if it is the same pump and whether it will run backwards.Running it backwards might help unclog it,or aid in diagnosis of a pump fault.
I was able to unclog the chicken soup pump by inserting a length of wire into the washer bottle filler cap and probing the area of the filter to remove some 'seaweed' . I then used a length of plastic pipe to repeatedly suck and blow water around the filter to clear it. Be careful not to swallow any, it tastes foul
I should imagine
(rather than fowl as in chicken.
) Better still use some sort of hose, but not too high pressure.