In-situ range verification of ion beams during dose delivery is a key for further improving the precision and reducing side effects of radiotherapy with particle beams. The detection and analysis of the emission point, time or energy of prompt gamma rays can provide corresponding means. Prompt gamma-ray imaging (PGI) has already been used for range verification in patient treatments with proton beams. The prompt gamma-ray timing (PGT) technique promises range verification at lower hardware expense with simpler detection systems superseding heavy collimators. After proving the principle, this technique is now being translated to the treatment room. The paper presents latest experimental results obtained with clinically applicable PGT hardware in irradiations of acrylic glass (PMMA) targets in pencil beam scanning (PBS) mode with proton beams at clinical dose rates. The data were acquired with multiple PGT detection units while the distal layer of an artificial 1 Gy dose cube treatment plan was repeatedly delivered to a solid PMMA target without and with a cylindrical air cavity of 5, 10, or 20 mm depth inside. The corresponding local range shifts were clearly detected and visualized by analyzing position or variance of the prompt gamma-ray timing peaks in PGT spectra assigned to the individual PBS spots. In this context, a major challenge concerning all prompt-gamma based techniques is examined and discussed: collecting the event statistics that is needed for range verification of single pencil beam spots at an accuracy level of a few millimeters.