I bet if you do the same test in the dark with the headlights off you will notice a slight lighting of the headlights with each turn signal flash. sounds like you are back feeding through the headlight circuit to get a ground.
I would verify that your turn signals front and rear have a good ground at each bulb holder. 4 double ended alligator clip wires about 24" long can be used to make a good temporary ground to each bulb holder.