Posting the solution for posterity:
Apparently, Lawn Tractors with this 14 + 2 pin control module are rather rare. The new Cub Cadets I have seen use the turning key style. Perhaps it is related to the fact that this is fuel injection engine. So, if you have a similar problem but a different model, then the problem is probably more likely to be something other than the module. If you have this model then check the safety switches, and the continuity to ground from the 14 pin Molex connector (as I described above) before spending money.
For me, a replacement reverse mow control module solved the problem. Mower works perfectly now.
I used a 725-06427A that I found on eBay for less than half the price of a matching part number module.
The original 925-06427A module (2063-003BB Rev 3 10-30-15) works 100% except it will not activate the PTO cultch.
