Multi-target multi-camera tracking of persons in indoor scenarios such as retail stores or warehouses enables efficient placement of products and improvement of working processes. In this work, we propose the ReidTrack framework, which performs the task solely based on peoples' visual appearances. In theory, accurate person re-identification is able to solve the whole task without the need for additional and complex scene models or post-processing steps. ReidTrack is based on clustering appearance embeddings with a mechanism to avoid identity switches caused by detection bounding boxes showing the body parts of multiple individuals. With only a robust person re-identification model and the real-time detector YOLOv8 and without any auxiliary information, such as complex scene models, our approach ranks fourth concerning Track 1 of the 2023 AI City Challenge.