In proton therapy, patients benefit from the precise deposition of the dose in the tumor volume due to the interaction of charged particles with matter. Currently, the determination of the beam range in the patient's body during the treatment is not a clinical standard. This lack causes broad safety margins around the tumor, which limits the potential of proton therapy. To overcome this obstacle, different methods are under investigation aiming at the verification of the proton range in real time during the irradiation. One approach is the prompt gamma-ray timing (PGT) method, where the range of the primary protons is derived from time-resolved profiles (PGT spectra) of promptly emitted gamma rays, which are produced along the particle track in tissue. After verifying this novel technique in an experimental environment but far away from treatment conditions, the translation of PGT into clinical practice is intended. Therefore, new hardware was extensively tested and characterized using short irradiation times of 70 ms and clinical beam currents of 2 nA. Experiments were carried out in the treatment room of the University Proton Therapy Dresden. A pencil beam scanning plan was delivered to a target without and with cylindrical air cavities of down to 5 mm thickness. The range shifts of the proton beam induced due to the material variation could be identified from the corresponding PGT spectra, comprising events collected during the delivery of a whole energy layer. Additionally, an assignment of the PGT data to the individual pencil beam spots allowed a spot-wise analysis of the variation of the PGT distribution mean and width, corresponding to range shifts produced by the different air cavities. Furthermore, the paper presents a comprehensive software framework which standardizes future PGT analysis methods and correction algorithms for technical limitations that have been encountered in the presented experiments.