I have not tried this, but it seems to me you MIGHT get a result (perhaps temporary) by back fushing it with a fine hypodermic syringe. (An insulin syringe has a fine needle).

Snag is that it'll probably re-block again. What tends to happen is that microbes grow on the detergent in old washer fluid (and more so in washing-up detergent if that's been used) to form a sludge, To fix that you might have to disconnect and flush out the whole system path.

I'd try to get at the jet where the fluid pipe connects to it, take the pipe off and check this delivers fluid when switched on. Check for gunge inside the jet, toothpick or cotton bud should pick it out, then use a fine wire from the outside.