Bigeye tuna generally are not accessible to recreational anglers because they travel far below the surface during the day. Only rarely are they seen on the surface, and then, only momentarily while feeding. This makes the fish hard to locate since they leave no telltale surface signs nor can they be easily located by trolling. Most bigeye tuna are taken incidental to albacore or marlin fishing. The best way to fish for them at the surface is to troll marlin lures in an area where the fish are known to occur.
That being said there is one method of fishing that does prove more effective for Bigeye Tuna and can result in the successfully targeting of Bigeye Tuna. Butterfly Jigging could be the answer to Bigeye Tuna fishing woes. Developed in Japan in the early 1990's to catch Bluefin Tuna in depths of up to 500 feet, Butterfly Jigging has been proven to out fish bait in many instances when the fish are finicky or just to deep for any other fishing method.
These jigs are widely known as the "butterfly" jig because of their distinctive flutter-like zigzag motion produced under the water. The jig moves this way because of the unique way the lure's edges are cut. Because of the sporadic movement and action produced by the "butterfly" jig, it entices fish to strike more often than traditional deep jigs.
There is a variety of different Butterfly jigs available but Shimano has the Butterfly Jigging System which utilizes tackle that is extremely manageable and lets you fight the fish more effectively rather than fighting the tackle.
If you can successfully locate Bigeye Tuna, and their depth then the Shimano Butterfly jig will probably result in a successful fishing trip.
All the sizes and instructions for fishing these Butterfly jigs can be found here;
Shimano Butterfly Jigging System