Coaching aims to unlock the human's potential, self-awareness and responsibility, improving the professional performances and the personal satisfaction. Its effectiveness is known to depend on the degree of bonding and mutual engagement of the coaching relationship. In this exploratory study we recorded synchronised EEG and SC data from both coach and coachee during 36 individual sessions, performed following 2 different coaching methods. Our principal aim was to investigate the temporal evolution of the bonding and the mutual engagement along the different steps of a session, by means of a "similarity" metric based on the DTW distance between signals (namely, S-TVM). We found significant differences between session phases for the EEG-related S-TVMs (BAR, BATR and AWI), with maximum values (defined as "tuning") all in the same phase, but differentiated between the two experiments. The results suggest a temporal concurrency of the engagement and emotional tunings, whose specific location seems to be a function of the coaching approach.