[old_tv_nut]

You don't have to believe me, but I suspected the next stage was a grounded-grid amp.
With the sharpness turned to minimum, current from V5A cathode is divided between the 39 ohm resistor and the cathode impedance of V5B at all video frequencies, so the circuit is actually lossy, current-wise, while R66 provides voltage gain. When sharpness is set to max, there is 139 ohms impedance at the resonant frequency of C48 and L15 (maybe tuned to about 2 MHz), which causes more of the current to go into the cathode of V5B. The bandwidth of the peak depends on the Q of the circuit, which is determined by the ratio of R4 at max (100 ohms) to the inductance L15.