Final answer:
While a mirror reflects light and could potentially allow a person to 'see' behind them, the practical application of such an idea is likely to be difficult and disorientating, despite the theoretical possibility.
Step-by-step explanation:
If we ignore the mythological aspect of the vampire and focus on the physics of light and mirror reflection, your idea makes sense. A mirror reflects light that falls on it into a specific direction and if that mirror is placed on the inside of an eyepatch, it would reflect what's behind the wearer into their eyes, provided the angle of incidence and reflection of light are maintained correctly. In this case, it could provide the wearer a form of 'eyes on the back of the head'. However, this is theoretical and would likely be very disorientating in practice.
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