You said that it doesn't matter which side -- the problem occurs on both the left and right turn signal.
So I'm thinking it may be a part that is common to both sides, like perhaps the flasher relay instead of the switch.

I had a recalcitrant turn signal once in a 240 -- only on the right side -- and it was the switch at the base of the turn signal stalk. The contacts were gummed up, and I fixed it by spraying with "tuner cleaner" (a spray used by electronic techs to clean electrical contacts).

But since it happens equally with both sides, I'm thinking that it could also be something else. Don't discount the switch (some other part of it common to both sides' circuits), but also consider other possibilities.

Good luck.