It's important to note that these probe models are very simple - they're "trained" by just doing a linear regression between the hidden activations and the desired output. This means that the probes can barely do any computation themselves, so if they work at all this is a strong indication that the signal they predict was already in the hidden activations.

For even more proof, see "Figure 5: Space and time neurons in Llama-2 models" for single neurons in LLMs that already encode this information, without even having to use a probe model to extract it.