1999 Dodge Dakota windshield washer will not spray

You will have to remove the air filter housing. You may want to try sticking a needle in the sprayer nozzle. They can sometimes become clogged and will cause issues.

For removal of resevoir follow instructions below.

Disconnect the battery negative cable.
Remove the air filter housing.
Remove the screw that holds the reservoir to the inner fender.
Remove the two screws that hold the reservoir to the cowl plenum panel.
Move the reservoir forward to access the pump wiring. Unplug wires from the pump and fluid level sensor.
Disconnect the supply hose and drain the reservoir.
Remove the reservoir from the vehicle.
Installation is the reverse of removal. Tighten mounting screws to 24 inch lbs. (2.7 Nm).

i had this very same problem. up close to the frogs there is a splitter that has a hole in the bottom of it as if something belonged in there. if you take that off and put a new one one that might fix your problem. check to see if it a problem by looking at it and spraying the fluid to see where it is leaking.