A complete solar eclipse is a pretty rare event, so it is tough to say how it might affect the fishing. However, check out this old letter published in the journal Nature from back in 1906. The author describes his experience while fishing during an eclipse in 1905 in Devonshire, England. From the sound of it, the bite improved dramatically! While its not particularly scientific, the writing from this time period is really entertaining.
There have been some other studies published about coral reef fish and herring, but the fact is, an eclipse is really rare, so there isn’t much information out there on how it might affect fish. Fish active during the day may start acting like its nighttime. Most studies agree that any effects only last a short time, and that fish go back to normal within a few minutes of the eclipse passing.
As a biologist and avid angler, I’d expect fish to act as they would during a typical sunset period. As the light gets lower, fish tend to feed more aggressively. With lower light, fish feed more confidently as they are less likely to be seen by predators and can better sneak up on their prey. As it gets dark, some fish stop feeding and find a spot to hide. Other more predatory fish like brown trout or catfish that are active at night, might bite more often. The bottom line is that its hard to predict how an eclipse will affect the bite. But remember, any effect from the eclipse is probably not going to last very long.
Either way, I’d be sure to back a rod before I head out of town!