A 'vacuum' is neither a conductor nor insulator. It acts a lot like semiconductor with no doping. If you put charge carriers into vacuum (electrons, or ions), the charge carriers can move through the empty space, conducting the electricity. If you don't put charge carriers into vacuum, there's no charge carriers and current does not flow.
In the insulator such as glass, charge carriers cannot move even if introduced. In the conductor, freely moveable charge carriers are present and can move. In the pure un-doped semiconductor, charge carriers are absent, but externally introduced charge carriers can move. The similarity doesn't end here. Even technological usage is similar. The field effect transistors are in many ways directly analogous to vacuum tubes. You can create 'depletion region' in semiconductor, which acts as insulator. You can create negative electric potential in vacuum, which will repel the electrons (so they won't fly in there).
Behaviour of insulators, conductors, and semiconductors is a lot more complicated than behaviour of vacuum, and it does not explain anything about vacuum to say that vacuum is either of those more complicated things.