I have had the same experience.
However, I changed the wiring on my toad and people are responding differently. The toad, a Subaru Outback, was wired for towing with the old school combination blinker/tail setup. After several of the incidents of seeming invisible turn signals I actually had the bride activate the signals to see if they were working and if they were visible. That's when it dawned on me that drivers could be expecting the yellow blinkers on the toad to blink, not the tail lights. It was an A Ha moment.
So, I went to the trouble to wire the toad with five wires, not four. Now the yellow blinkers blink just like they would if I signaled from the car. Other drivers seem to react better to that.
Any way, it's something to think about.