Oil pressure and flow that actuates the cone clutch is controlled by an electric solenoid valve which presses a little steel ball against an internal oil control port. Some OD failures are a result of electrical failure of the shifting solenoid. So it is appropriate to use a jumper wire to apply power to the solenoid to see if it will operate (usually with a loud click). The solenoid has two wires for power and ground, and it is not polarity sensitive. If the solenoid does not click when the control is switch on, but does click when using jumper wires, then look for the fault in the switch(es) or harness wiring.

If the solenoid does click, but the OD does not shift, then the fault is inside. The most common problem here is a clogged oil pickup screen, which is accessible by removing the external cover. The second likely cause is some clog farther up the oil flow passages, or a flow director ball that does not seal on the port when it clicks (possible dirt in the control valve). These problems are commonly fixed by cleaning the parts, accessible by removing the external cover.

When the solenoid clicks, and you have checked and/or cleaned the filter and valve parts, and it still won't shift, then the fault might be failed seals in the co-axial piston that moves the cone clutch. If the OD unit shifts but will slip profusely, this may also be faulty piston seals. Or the cone clutch friction material might be worn out an in need of replacement. These problems require disassembly of the unit for replacement of the failed parts. Good news is that the internal faults of the cone clutch are very rare, and most of the control problems can be fixed from under the car without removing the gearbox from the car.

Some MGB have an overdrive control switch in the top of the hand shift lever with a wire(s) running up through the tubular lever. Occasionally that wire(s) could get abraded and break or short out on the shift lever, in which case the OD wouldn't work (usually permanently down-shifted). That seems to be one of those good ideas that was poorly executed in design. If you want the switch to be somewhere else not on the shift lever, then consider that most later model MGB had the OD switch incorporated in the multifunction switch along with the turn signal switch. This switch and most of the harness wiring were there even in in all cars including cars without OD. Earlier MGB had a toggle switch on the dash for OD.

For the simplest control wiring power comes from the ignition switch on a white wire to the manual control switch, then to the solenoid, then to the gear selection switch, then to ground. The gear selection switch is to prevent operation of the OD unit unless it is 3rd or 4th gear (4th gear only on later cars). If you would jump wire power to the solenoid, it needs to be in 4th gear to make the ground connection. Otherwise you need two jump wires for power and ground.

For a gearbox on the bench you also need two jump wires, power to the solenoid and ground. Put power to the solenoid, and ground the second solenoid wire. Otherwise there is a wire running from the solenoid to the gear selection switch, and the selection switch has to be grounded, and it has to be in 4th gear to close the switch to complete the ground connection.

For early model MGB with D-type OD there may be a couple more electrical devices in the circuit, like an OD relay and a throttle or vacuum switch. Check the MGB wiring diagrams for the appropriate model.

I was once helping a friend diagnose a non-functional overdrive in his MGB. We first had to install a known good solenoid to replace one that did not work. Then after a little fiddling the solenoid would click with ignition on and manual switch on and gear selector in 4th gear. But it refused to work on the road. Connecting a jumper wire with extra manual switch to supply power directly to the solenoid had it working on the road. The problem turned out to be a mismatch of parts in the snap connectors at the solenoid wires such that the snap connectors had intermittent contact. It was a very simple problem and simple fix, but the diagnostic work was tricky (time consuming).