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Without the cable, the transmission will tend to upshift as soon as possible (as if you had let up off the gas pedal), possibly good for gas mileage. And don't worry about what happens when you slow to a stop -- the transmission will shift down back into first for a proper getaway, at least up to a few miles per hour, when it will upshift more quickly that you might prefer (but again, only as soon as if you had just lifted off the gas pedal in a normal car).

However, as you noted, you won't have any "emergency" kick-down or downshift for acceleration via the gas pedal -- the tranny will ignore your call for a downshift via the gas pedal. Thus, if you need the benefits of a 4/OD to 3 downshift, you need to get the OD system fixed. Likewise, for a prompt 3 to 2 (or even a 4/OD to 2) downshift, just pull the shifter back toward you.