Either to Sign ----The mandate as provided to the Bank stands, anything to the contrary could expose the Bank to allowing the account operate outside the agreed t/c's as contained in the mandate, the purpose of the mandate is to protect all parties, there are no ad hoc agreements as to how a joint account should operate and advising the Bank of a change of circumstances should as these by word of mouth is worthless.
Without specifics it is hard to advise further but I'll speculate, If an elderly person is the joint account holder then it is reasonable to assume if that person becomes incapacitated then they understood that the other party would have control, that is not unreasonable, the mandate stands until formally changed or until one party to the mandate dies.
Both to Sign - This is a very unusual mandate, possibly an older longstanding one, Banks don't accept such instructions today, the accounts are far too difficult to administer, if this were to happen as you have outlined then the account would be frozen with no debits permitted, not by word of mouth alone, documentary evidence would be required again to protect the Bank.