I have never personally seen or ever heard of one without the flap on the back, so I am going to say no they didn't. Looking at the Model #1, Model #1A, and Model #2 Operator's manuals, there is no mention of nor picture of one without a flap on the back. These manuals may be found in the Resources section of the forum, under "Technical Library -- Implements" for your further review.
I enlarged your picture to the capability of my computer and it appears that you can see discoloration of the rusty areas on your main tiller where the rod holders once were located.
Cub Cadet 123
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Still don't know what I'm doing in OHIO?.....If you find me, then please point me back toward INDIANA. 
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