Psychology laboratories used to (and maybe still do) experiments involving rats or mice and mazes, to figure out how the brain learned. The experimenter would put some sort of treat (like cheese) in one part of the maze and see how quickly a rat would be able to find his or her way there and so on.
However, being a maze, there were a lot of dead ends, or ‘cheeseless tunnels’ without any prize or treat at the end. So when someone says they’re going down cheeseless tunnels, they’re saying that they’re doing a lot of work without any reward.
I should note, though, that this is not a very common expression in English. J
쥐가 치즈가 없는 터널에 들어 갔으니 열심히 했으나 아무런 보상도 없는 헛수고를 한 거네요...ㅠㅠ