Well it might have helped if they were a little more specific instead of saying it is an electrical problem.
Indeed the overdrive shift is done through a ground supplied by the PCM when the proper conditions are met. In most cases this is determined by several signals including engine temp, engine speed, engine load, vehicle speed and throttle position. This is why I am saying they should have been a little more specific instead of telling you it is an electrical problem.
One of the regular mistakes made by some transmission shops when rebuilding the A500 transmission is the improper installation of the spring for the 3-4 shift timing valve in the throttle body. It is very easy to install it backwards and it will fit just fine. However it puts the wrong end against the spring.
If you are determined and want to check the electrical system of the Overdrive circuit yourself, it is not terribly hard. Try this--
turn on the ignition. Ensure that the overdrive cancel switch is off. Back-probe the PCM terminals 55 and 37. There should be 12 volts present at both terminals. If there is no voltage at terminal 55, check the circuit between the PCM and the overdrive cancel switch or overdrive cancel module.
Back-probe the PCM at terminal 10. Check for 12 volts with the overdrive cancel switch off and zero volts with the overdrive cancel switch on. If the voltage at terminal 10 does not work as described, check the overdrive cancel switch or overdrive cancel module.
If the voltage works as described, but the overdrive does not work, check the TPS, engine coolant temperature sensor, vehicle speed sensor and park/neutral switch.