You have a bulb in the toad (left side) that is getting it's ground through the filament of another bulb or through the second filament in the same bulb. (i.e. poor ground somewhere, or shorted bulb) Check all the bulbs and socket connections in the toad tail/signal lights.
The reason the problem shows up only when the head lights are on is because the available voltage drops and the flasher is not seeing the required load current to make it flash.
I'll even go out on a limp and guess that your toad has amber turn signals and your motorhome does not. You are using the normal brake/tail light in the toad as the signal light also. right?
This is all speculation of course:)