Its a simple test to narrow down the cause.
There is a good site on the web called toiletology or something similar. If you can find it on a web search check it out. you can read through a lesson plan or jump ahead and review the index and link to pages. Pay special attention to the sections mentioning the "mystery flush". I've simply advised you to the step two of trouble shooting that fits your description of the "symptoms of problem" that follows your findings after the step one diagnosis of the food coloring in the tank test, colored water in the bowl test.