Transition crossing in the CERN PS is critical for the stability of high intensity beams, even with the use of a second order gamma jump scheme. The intense single bunch beam used for the neutron Time-of-Flight facility (n-ToF) needs a controlled longitudinal emittance blowup at flat bottom to prevent a fast single-bunch vertical instability from developing near transition. This instability is believed to be of Transverse Mode Coupling (TMCI) type. A series of measurements taken throughout 2009 and 2010 aims at using this TMCI observed on the ToF beam at transition, as a tool for estimating the transverse global impedance of the PS. For this purpose, we compare the measurement results with the predictions of the HEADTAIL code and find the matching parameters. This procedure allows a better understanding of the different mechanisms involved and can suggest how to improve the gamma jump scheme for a possible intensity upgrade of the n-ToF beam.