It appears that in binnie-mods-1.12.2-2.5.1.188.jar (I have not looked at previous versions) that the fence recipes are somewhat confused. The Full Fence and Low Fence recipes seem to produce each other's item. Also the Wood Plank positions in the Full Fence recipe give the opposite expected fence color configuration in the output item.

Also, I assume as a side effect, JEI is labelling the Low Fence as the Full Fence and vice versa.

Another related item, for which I have put in a request to Quark, is that the Full Fence recipe conflicts with Quark's Chute recipe which, in my modded Minecraft game, completely masks the Full Fence recipe.

So there is quite the tangle here...if someone wants to craft a Full Fence they will have to actually craft what JEI calls the Low Fence and if they want the Low Fence they will craft the Full Fence per JEI and then also discover they must reverse the expected Wood Plank positions to get the correct resulting color orientation on the output Fence.

I think I see the problem in FenceType.java in getPrefix() in the first if statement...for the reversal of the Full vs the Low Fence recipe name...or is it in MultiFenceRecipePattern.java where the array VALUES defines the recipes and the array members 2 and 3 should be swapped with members 4 and 5?

Having gone through the effort to actually craft all of the single wood fences, I can say that the issue is that while the recipes are correct for the Low and Full fences the names have been reversed.