In order to remove the cooldown from the Rods, you will need the artifact called "Magic Scepter". When you get this, the cooldown on any Rod will be completely removed. This means that you will be able to hold down the mouse button with the Necro Rod to spawn Skeletons for as long as you hold it down, or use the other Rods to permanently shoot fireballs and what not.
This Magic Scepter is needed if you want to set up a Lighthouse farm where you grind insane amounts of Bones to get XP and Coins fast.
How to get the Magic ScepterHere's how you get the Magic Scepter to remove the Rods' cooldown. First find the NPC called tthe Wizard. He will spawn at a random island in the Fire Biome. Since the islands are randomly generated, there is no way of telling exactly where he will be located, so just buy more and more islands until you eventually stumble upon him somewhere in the Fire Biome.
When you find him, he will offer you his first quest. You will need to find 20 x Cinderbloom and give them to him. These also spawn in the Fire Biome, so just run around and loot them, then return to the Wizard when you have all 20 of them. Now he will give you yet another quest, but this time he needs 20x Green Pigment.This Green Pigment is created at the Inscription Table when the skill "Novice Scrolls" is acquired, and requires a total of 200 Cactus Fruit, 200 Jelly, and 200 Seaweed for all 20 of them! This might take a while to get your hands on, so make sure to put down some Fish Traps before you run around and look for Slimes and Cacti.
When you have this, turn it in and accept the third and final quest he will offer. This time he wants 200 x Crystals. This is a resource that is obtained by mining crystals in the Winter Biome, so make sure to unlock at least a few of the Winter Biome islands to get enough Crystals.
When you have completed the third quest, the Wizard will gift you the Magic Scepter artifact, and permanently remove all the cooldown period from all your Rods.