Can a current be induced in an HDMI cable that runs parallel to a 120v AC cable for 15 feet?
The coupling could result from a Y-capacitor in the HDMI switch power supply. A Y-capacitor is placed between L-GND and N-GND and often used to filter out common-mode noise and to establish a common ground reference (with respect to "earth").
If the outlet / plug does not provide proper grounding (only N and L connected) and you touch GND on the HDMI cable, there might be a small current between flowing from L-GND-YOU-EARTH. Y-capacitors are tested to applicable standards to qualify them as safe. They never fail as "short" and there are typically only a few uA flowing, but it is enough to feel a tickle.