ATC, like we do, take their role seriously and are rarely bored. They would not have considered any call from Essel as entertainment but would have done their best to help. That is their job!
Just wondering. How much of 'Aircraft Technical' subjects do ATC get in their training? If a pilot calls "I have a small problem: I have a vacuum pump failure" would ATC be able to infer that this, most likely, means that the DI does not work and that turning onto a heading becomes far more complex, particularly for a low-hours PPL?
If ATC would have known that the DI was inop and turning onto/maintaining a heading was more complicated, they probably would have warned before the infringement happened.
Another mitigating circumstance might be the following: The indication that something was wrong with the vacuum was the AH toppling. Now the AH and DI both need gyros to work, and both gyros will take a few minutes to spin down once the vacuum is removed but they will not start indicating wrongly at the same time. It might just be so that the DI was already showing a serious error before the AH toppled, and that the OP was way off course by then already.
Essel, you said you headed directly for the overhead of the nearest airfield. How did you navigate there? Was that all visual, DR, GPS or what? Since you infringed by two miles, I am lead to believe that you were quite a ways off from that field and possibly used the DI to navigate to that field. Did you realise that your DI would be off, did you use the compass, properly?
On the other hand, since this is officially an ongoing investigation, it might be best not to comment too much on this, right now.