The Stoplight Loosejaw is one of the samples you'll need to collect for the Researcher in Dredge, but it's not immediately obvious where to look. The Researcher gives you "pursuits", or quests, that task you with collecting samples of different marine life, though you won't have many clues about where to find them.
It's not all plain sailing, either. There are many dangers out in the ocean, and you'll need to take care of your boat if you want to keep it and your fishing business afloat. Making repairs at a Shipwright or upgrading with refined metal (opens in new tab) is a good place to start, but you can find other things to make your seaborne life easier, too. So without further ado, here's the Dredge Stoplight Loosejaw location and the reward for giving it to the Researcher.
Dredge Stoplight Loosejaw location and reward
The Researcher that asks you to locate and bring them a sample of the Stoplight Loosejaw is found at the Old Fortress, an outpost found to the northwest of Stellar Basin. When venturing that way, be careful not to sail too close to the centre of the basin area, as a large octopus (squid?) appears to have taken up residence there and is fully capable of completely destroying your boat if you hang around for too long.
Thankfully you won't need to worry about getting tentacle-slapped to get your hands on the Loosejaw. Head north and slightly east of the Old Fortress and watch for a collection of small red lights beneath the water's surface indicating the Stoplight Loosejaw fishing location—check the screenshot above if you're unsure. It doesn't matter what time of day or night you choose, and you'll need a rod capable of Abyssal fishing in order to catch it.
Once you have the sample, along with the others needed for the pursuit, return it to the Researcher at the Old Fortress to receive the A Plan for the Future book which, when activated, gives you a 15% chance to not reduce fishing stocks when using a rod.