My bet it's induced, not a direct connection otherwise you would have gotten A LOT more than a tingle.
To find out, clamp the meter lead to the gutter and the ground so it is reading without you having to touch it, clamp a wire to a ground rod in the dirt OR (2nd choice) take that ground pin of the extension cord you mentioned, put on a pair of gloves, stand on dry cement or wood, hold the grounded wire in one hand, put the other hand in your pocket and jam that grounded wire on the gutter while looking at the meter.
If the voltage goes away when you ground it but returns when you lift the ground then it's induced. If you get a BIG spark then nothing (maybe breaker tripped) then it's pretty much a direct connection (a so-called "short"....I hate that term) and that will be harder to find AND can be pretty dangerous until found and corrected.
Had many a street light exhibit induced voltage like that from nearby overhead primaries of 18KV to 60KV and the pole's bond wire was loose or had high-resistance from corrosion.