Are you sure both vac's are running, i can't see how both can be powered from the one switch, unless it's always done this.
More likely one is spinning the other, as they are series mounted. Carefully remove one wire from one vac motor, ensure it is safe from earthing, then switch on, after that replace the wire, and take one from the other motor, i suspect that
you will find it dead when one of the wires is removed. That will tell you the other motor is not working.
I wonder if it's one of the cheap chinese motors mentioned in an earlier thread.