I do think linear probes are useful, and if you can correctly classify the target with a linear probe it makes it more likely that the model is potentially “representing something interesting” internally (e.g. the solution to the knapsack problem). But its not guaranteed, the model could just be calculating something else which correlates with the solution to the knapsack problem.
I really recommend checking out the deepmind paper I referenced. Fabien Roger also explains some shortcoming with CCS here. The takeaway is just, be careful when interpreting linear probes. They are useful to some extent, but prone to overinterpretation.
I would also assume that methods developed in challenges like the Trojan Detection Challenge or Universal Backdoor Detection would be good candidates to try out. Not saying that these will always work, but I think for the specific type of backdoors implemented in the sleeper agent paper, they might work.