This skill is covered in the partial panel work during IR training.
You use the turn and bank with reference to your compass to maintain wings level.
And vsi cross referenced to ASI to remain level or hold a climb rate
The whole trick is to remain trimmed and only alter 1 thing at a time.
As with all flying its important to aviate navigate communicate
So if you did have a vacum failure, which is actually pretty hard to spot if you are concentrating on other things.
Its important to fly the machine and to establish yourself above MSA, wings level, and trimmed for level flight pointing in a direction which means your not going to hit another plane (ie controlled airspace) or hit anything on the ground.
Then tell ATC, personally i would declare a mayday, but even if you didn't i am sure that ATC would give you the same service what ever you declared. They would then try and get you somewhere to land or into VMC.
In a failure just afteroff you would maintain wings level then by small adjustments of pitch hold your climb speed. Then unless your going to hit something, climb straight ahead.
RT " MAYDAY MAYDAY MAYDAY G-XXXX Instrument failure climbing staight ahead to y000ft standby"
The standby is important because otherwise ATC will come back to you and start asking questions when you should be putting your full attention into flying the machine. If they do start asking questions which are not critical to the situation ignore them. ie whats the number of POB and the like. But if they say give you a flight safety instruction then respond.
Then once you are above MSA and trimmed and settled. Call ATC again and with there help decide what would be the safest option.
As with all these skills currency plays a big part to the end result. Last year I hadn't flown IFR for 6 months, my scan, and handling were utter pants. After a not very impressive trip I made sure that got at least an hour a month in IFR and during the trips practised partial panel (but not the unusual attitudes stuff) but to be honest even that wasn't enough.
Its all covered in the instrument Thom book.
The contents of this post in no way are meant to comment on the incident.
And my condolences to anyone who knows the deceased.
MJ