Clearing Faller Cement Needle Applicators
In addition to dipping the tip in solvent, try a lighted match under the tip for a few seconds. Alternatively, a fine wire (such as those used by 1/35th scale armor modelers to assemble workable metal tracks for tanks) works quite well. Feed the wire into the shaft about 1/8" at a time, slowly, such that you don;t kink the wire. Eventually it will pass all of the way through and clear the plug.
Tip for not getting the shaft applicator clogged: Frequently clear out the inside of the plastic cap of dried adhesive that gets pushed into the tip when the cap is placed back on the bottle. Also, if you drag the applicator tip along a seam to apply cement, make sure that you clean the tip of any residue as that will form a plug as well.
Don't give up on this fabulous adhesive, which is a lot easier to apply accurately than any liquid with a brush!