Distaff. If the 'bank and slip' indicator you mention could give you a rate of turn then it was, assuredly, gyro driven. Even the Tiger Moth has one of these in the centre of the instrument panel. You don't need a vacuum pump, just a venturi somewhere on the fuselage. These normally look like a short cone and a long cone joined tip to tip. This system is nice and simple but relies on you having some airspeed and so won't work on the ground.
The use of venturis reminds me of a story, probably apocryphal: on the Harvard there were 2 venturi, one big one for the instruments and a small one to ensure that users of the p-tube didn't get their own back. Once day a big, instrument one was accidentally fitted to the p-tube and an unfortunate pilot experienced the 'Chartham Method' unexpectedly. He had to slow down to the stall to extract himself from the predicament. Makes my eyes water just to think of it!