Speaker embeddings are promising identity-related features that can enhance the identity assignment performance of a tracking system by leveraging its spatial predictions, i.e, by performing identity reassignment. Common speaker embedding extractors usually struggle with short temporal contexts and overlapping speech, which imposes long-term identity reassignment to exploit longer temporal contexts. However, this increases the probability of tracking system errors, which in turn impacts negatively on identity reassignment. To address this, we propose a Knowledge Distillation (KD) based training approach for short context speaker embedding extraction from two speaker mixtures. We leverage the spatial information of the speaker of interest using beamforming to reduce overlap. We study the feasibility of performing identity reassignment over blocks of fixed size, i.e., blockwise identity reassignment, to go towards a low-latency speaker embedding based tracking system. Results demonstrate that our distilled models are effective at short-context embedding extraction and more robust to overlap. Although, blockwise reassignment results indicate that further work is needed to handle simultaneous speech more effectively.