Mental imagery has long been of interest to the cognitive and neurosciences, but how it manifests itself in the mind and brain still remains unresolved. In pursuit of this, we built a spiking neural model that can perform mental rotation and mental map scanning using strategies informed by the psychology and neuroscience literature. Results: When performing mental map scanning, reaction times (RTs) for our model closely match behavioural studies (approx. 50 ms/cm), and replicate the cognitive penetrability of the task. When performing mental rotation, our model's RTs once again closely match behavioural studies (model: 55-65°/s; studies: 60°/s), and performed the task using the same task strategy (whole unit rotation of simple and familiar objects through intermediary points). Overall, our model suggests: (1) vector-based approaches to neuro-cognitive modelling are well equipped to re-produce behavioural findings, and (2) the cognitive (in)penetrability of imagery tasks may depend on whether or not the task makes use of (non)symbolic processing.