The simplest of all fountain pens, dropper-fillers (often called simply "eyedroppers") have no internal filling mechanism of their own. Most open by unscrewing the section, after which the barrel is filled with ink using a rubber and glass dropper. Leakage at the joint should not be a problem if the threads are kept clean. A light application of beeswax or silicone grease to the threads can give an additional margin of security. Dropper variants include the Parker Jointless, in which the section assembly essentially fits like a plug into the end of the barrel, and the aptly-named middle-joint, where the pen unscrews in the middle.
Retracting-nib safety pens also fill with an dropper. To fill, hold the pen cap end up, then unscrew the cap. The nib should already be retracted inside the barrel, allowing ink to be introduced through the open barrel end. Once filled, the a safety should not be capped or uncapped unless held upright, otherwise the ink will pour out of the open barrel. Always remember to retract the nib before replacing the cap!
Many Japanese dropper-filling pens have a distinctive ink shutoff system utilizing a central shaft attached to a knob threaded onto the end of the barrel. These pens are often mistaken for plunger-fillers but they lack a piston seal and must be filled manually. Screwing the knob down all the way forces the stopper at the end of the central shaft into a recess in the feed, cutting off ink flow. Before writing, the end knob should be unscrewed slightly (usually just a partial turn) to open the valve. This is also advisable before removing and replacing the section when filling, as this will reduce the stress placed on the central shaft. In normal usage there is no need to fully unscrew the end knob and pull out the shaft. If there is leakage around the shaft, repair procedure is similar to that for Onotos.
Original 1920s Waterman eyedropper instruction sheet.
Original 1920s Waterman safety instruction sheet
Pen Profile on Jointless, middle-joint, and end-joint eyedroppers