In Palworld, crafting schematics for legendary fishing rods can be obtained randomly by opening chests found in high-level Syndicate sea bases, or by salvaging piles of scrap floating in the ocean. There's going to be a fair bit of luck involved in both of these methods, and the latter will also require a small resource investment, as you won't be able to fish up salvage piles in Palworldwithout using craftable fishing magnets.
Palworld: Legendary Fishing Rod Schematics Location
You can sometimes get crafting plans for legendary Depresso fishing rods by raiding Syndicate sea bases or gathering salvage from the ocean using Powerful Fishing Magnets. These two methods have their own set of caveats, but they're well worth trying if you really want to get an upgrade for your fishing rod.
Syndicate Sea Bases
While exploring the open ocean, you may stumble upon floating bases occupied by Syndicate members. These bases are much like the bases you find on land; they're full of heavily-armed Syndicate enemies, and you'll find a bunch of treasure chests inside them too. In my experience, the chest at the very top of each Syndicate sea base has the highest tendency to drop Legendary Fishing Rod schematics in Palworld, though the chests on other levels of these bases might also drop them as well.
I've marked the location of the sea base where I found my first Legendary Fishing Rod schematic above (coordinates: -343, 808). The game won't render the base until you're very close to it.
The enemies here are level 55, so bring good equipment or a strong flying/swimming Pal with you. I usually mount my Neptilius when exploring the ocean, though you can easily use a flying mount like an Eidrolon or Jetragon too.
Once cleared, hostile NPC camps reset after 30 minutes. If you failed to get a Legendary Fishing Rod schematic the first time, come back in half an hour.
Salvaging Method
This works exactly the same way as Coralum farming in Palworld. Grab an Advanced Fishing Rod, some Powerful Fishing Magnets, and ride a swimming mount into the open seas and look for floating piles of garbage on the water. Approach the pile while on your swimming mount, then interact with the pile to start reeling up loot. This consumes one Powerful Fishing Magnet every time you do this, so you may want to bring a few dozen of them.
While you're fishing with magnets, you might as well bring a Jellroy with you. If you have one in your party, you'll get more materials than usual. I'm not sure if this actually increases your odds of getting a Legendary Fishing Rod schematic, but you'll at least get significantly more of every other material you get from floating salvage piles.
I got a fishing rod schematic by gathering salvage in the ocean near the Syndicate base noted above. Other players have reported finding the legendary schematics by fishing near Feybreak, so if you're not getting any luck up north, try fishing down south.