Looking at the 556 circuit at http://www.eld.leidenuniv.nl/~moene/Home/museum/Bondwell12/schematics/BW12-A1-CPU-IO-Decode.pdf
, I'm trying to figure out what they were trying to do here.
It seems they basically used the 556 as a fancy voltage threshold comparator with hysteresis; the IC51 7416 open collector inverter pulls the TRIG and THRESHOLD pins low when its input (MOTOR1 | MOTOR2) is high, which makes the OUT pin of the 556 high and leaves it that way (which turns on the motor). When the (MOTOR1 | MOTOR2) signal is low, the 7416 allows the TRIG/THRESHOLD pins to be charged (via the 100k resistor at R16 to VCC, charging the capacitor at C11 which is, I think, 1.7uf electrolytic) until the THRESHOLD pin reaches 2/3 of VCC at which point the 556 shuts off and turns off the motor.
This is a non-standard hookup of the 556, since normally the capacitor is between the threshold/trigger pins and ground, not between them and VCC. The 556 is basically being used only for hysteresis (turns on when trigger is below 33% of VCC, turns off when threshold is above 66% of VCC) with the trigger and threshold pins tied together, and the external circuit with the 7416 discharging C11 and C11 recharging through the 100k resistor.
Since the 7416 pulls directly to ground it should discharge C11 very fast (and this current surge is probably not great for the lifespan of either C11 nor the 7416, though the 7416 is meant for very high voltage applications so it may be ok), however this discharge rate technically controls how fast the motor will turn on after request, so it is a finite (but very small) delay, which might be able to be ignored.
So, for the old fashioned τ = RC time constant equation for how long a capacitor takes to charge to ~63% of its capacity (and assuming 63% and the 66% of vcc threshold for the 556 are 'close enough' to be the same), the motor off delay is ~0.17 seconds.
This should be easily emulatable using a timer.