Different from existing cross-modality identification tasks (e.g., heterogeneous face recognition, sketch re-identification, etc.), we introduce a novel yet practical setting for these related identification tasks, named \textbf{sketch biometric identification}, which aims to continually train a unified model across different data domains, even diverse identification tasks. Sketch biometric identification faces challenges, including scarce real sketch data, high annotation costs, privacy risks, and insufficient generalization ability of cross-task models. Existing methods usually rely on limited real data or single-task optimization, making it difficult to effectively address the joint challenges of cross-modality and cross-task. This paper proposes a unified framework that integrates efficient synthetic sketch generation and task-sequential continual learning. First, we design an efficient pipeline to generate a large-scale and high-quality synthetic person and face sketch data, which significantly reduces costs and avoids privacy risks. Meanwhile, we enhance the model's robustness by fusing real data. Second, we construct a universal unified framework for sketch biometric identification, which adopts a task-sequential training strategy: the model first completes sketch person re-identification learning on the person dataset; subsequently, it maintains the acquired person recognition capability through a trusted sample replay technique and seamlessly performs incremental training on the face dataset. This enables a single model to simultaneously handle the cross-task capabilities of multiple sketch biometric identification tasks. To support the study of the mentioned sketch biometric identification, we built a new large-scale benchmark, SketchUnified-BioID, with several practical evaluation protocols.