In Exodus 4 Yahweh gives Moses a sign to perform before the elders of Israel: he is to cast his rod down so that it turns into a serpent (Hb. “nachash”). He is also to perform this and the other “wonders” before Pharaoh (4:21). Of course “nachash” is the same kind of serpent that tempts the woman in Genesis 3, and interestingly, Revelation calls that serpent of old a dragon (Rev. 12:9, 20:2), suggesting that even the “serpent” that Moses’ rod turns into may be something more than your garden variety garter snake.
But there’s more: in Exodus 7:9-12, Moses and Aaron go before Pharaoh and Aaron throws down his staff and it becomes a “serpent” (Hb. “taneen”) that swallows up the “serpents” of the Egyptian magicians. You’ll notice though that “taneen” is a different word from the previous “serpent” word (“nachash”). “Taneen” is not merely a snake; “Taneen” is a great sea monster (Gen. 1:21, cf. Is. 27:1). Thus, when Moses/Aaron throws down his rod it probably becomes something much larger and frightening than a mere snake (which better explains Moses’ reaction in 4:3). Moses’ rod turned into something much more akin to a dragon.
Finally, it’s Ezekiel who picks up this imagery explicitly calling Pharaoh a dragon, a great sea monster in the midst of the Nile (Ez. 29:3, 32:2). Of course Ezekiel is speaking about a different Pharaoh historically, but the symbolism is all still there. The Pharaoh of the Exodus and all other oppressive Pharaohs are the “seed of the serpent” or better, the “seed of the dragon.” And thus Pharaoh is a dragon, a sea monster in the midst of the Nile River. But Yahweh intends for Moses, his servant, to take this dragon by the tail. It’s astonishing enough that Moses would tame a snake by taking its tail (usually one goes for the neck right behind the head). But now, we are not dealing with a little garden snake or even a boa or a python. It’s probably something at least more terrifying if not actually larger and fiercer. And yet Moses will take it by the tail.
All of this is ultimately what Yahweh is doing with Pharaoh. He is using Pharaoh, the sea dragon of Egypt as his rod to lead his people to the Promised Land. He is using Pharaoh as his tool to shepherd his sheep. And since he is Yahweh, he takes Pharaoh by the tail just as though he were a little garden snake. And when Yahweh is with his servants, he does this through his servants.