A few simple rules!
Aviate, navigate & communicate is most certainly not 'old tosh'. For those three simple words give the best guidance to any pilot when faced with a dilemma, whatever the experience level.
Aviate - will include; completing FREDA/LIFE (whatever) checks. Identification of the fault and isolation of the problem. Evaluation of the consequences of the failure; requirement to fly on a limited panel and by reference to the 'E' type compass for heading.
Navigate - will include; knowing position, deciding on the plan of any action required: divert or to continue with the flight as planned.
Communicate - Inform air traffic. In this instance the level of assistance required will depend on the factors identified during the first phaze and the complexity of the second. In the case of a vacumn pump failure the conditions may determine. Should the visibilty be very poor and the pilot is without a discernible horizon, perhaps surrounded by open seas, high terrain or controlled airspace then an 'urgency' call should be made immediately as it also should be if you find yourself overwhelmed in whatever conditions. However Essel appears not to be concerned about any of these factors. Simply having informed the FIS would have been all that was needed and would most likely have avoided the resulting infringement.
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!