I think it probably is a special texture, as look in the Minecraft folder, and you see 5 special texture files, 0 being of the highest quality. There the pink-and-black-checkered is, down around the bottom-right corner.
Actually, now thinking about it, I wonder why it appears as a pink-and-black-checkered pattern if it can't find the texture for which it is looking. It could be a special texture or code which makes it look like that.
I think it probably is a special texture, as look in the Minecraft folder, and you see 5 special texture files, 0 being of the highest quality. There the pink-and-black-checkered is, down around the bottom-right corner.
pack_0-1 is the version where the 'top' of the furnace is also the top of the dropper and dispenser.
pack_0-2 is where I tried to insert a new texture and use it, but failed.
I tried downloading a 3D modeller and rebuilding the droppers and dispensers with the added texture; it, however, ended in the same result as pack_0-2. I used MrCrayFish's 3D modeller. That is what's in pack_0-3.
Tell me if the file, 'dropper-top.png' is not there.