$100 Special - No Reverse; Help/suggestions Appreciated

[The Push mower]

Craftsman LTS2000 (917.289081). I followed the shifter adjustment procedure in the manual and forward works great now, but reverse does not engage at all. After about 10 minutes of messing with this thing the main drive belt jumped off twice so I simply slipped it back on and forward works fine.

Inspected the shifter and linkage and did not find anything apparently broken.

Any ideas?

 

[mechanic mark]

Remove deck,scotch front wheels, jack up rear & place jack stands for safety so you can pull both rear wheels & inspect axle for missing keys. Use a wooden 2x4 between jack & transaxle so you will not crack or break aluminum transaxle housing. If keys are in axle shaft have a helper start tractor & try to put in reverse while you are looking for problem. Safety First,Please be careful with moving parts, axle shaft, belts, etc. Always use Craftsman OEM parts. Let us know what you find, thanks, Mark
Apply antiseize compound to axle shaft both sides before reinstalling wheels.

https://www.searspartsdirect.com/model/1tawhjtqb5-000247/craftsman-917289081-front-engine-lawn-tractor-parts

 

[The Push mower]

Found both keys on rear wheels and all present/good. Sadly, it is one of those General Transmissions made of plastic.

GT ID sticker is gone and the stamp on left output axle tells me nothing about which transmission exactly I am working with. Cleaned trans good and when I tried to remove the pulley via 4-T20 screws a cable came loose and a rusty spring fell out. Now the cable #12 is dangling and totally disconnected. My guess is this a drive control cable...? The diagram is so poor in quality I can't make out where this spring goes. This same cable #12 is identified as a "hood cable" on the transaxle diagram. UGH! I believe #12 is the drive control cable, but....

https://ibb.co/sFt4m2h
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