SOLUTION... potentially
I fixed my TOA-60 without replacing the FZ31-9E (11pin,7pos) rotary switch. I think it will work for you too if your units switch failed in the same way mine did. Mine failed by melting the switch housing around the pin where the power connects (pin B on the rear half of the switch).
I fixed the unit by bypassing that part of the switch and tying the brown power wire (from the door switch) to the two white wires above it (pos 3&4, go to the two timers). This will make power go to both timers for all functions...so only use 1 timer at a time or the longer timer will set the duration.
I pulled the unit apart. Traced all the wires and made a diagram). Tested continuity across all the switch pins to understand the functions and made a table). Also, found the hua li lai web page and realized the switch must be custom for Cuisinart...so I doubt it can be found online anywhere.
http://www.hualilai.com/eprojgt.htm ...these are tables showing contacts for their standard switches.
I realized that the switch's 4 separate inputs each only connects to 2 outputs each across all 7 positions. That means that the rear half of the switch is only functioning to determine which timer the power goes through. So connecting those 3 wires only means both timers will send power for all 7 positions.
This will only work if the one of the pins B/3/4 of the rear half of the switch has failed.