From my notes
ENGINE CONTROL LEVER (ECL) ECL 1 and ECL 2 are installed on the overhead console. They are connected to the respective engine control gearbox, through a power control cable. Each engine control gearbox is mechanically connected to the respective Fuel Management Module to permit controlling the engine power manually in case of critical failure of the EEC. When an ECL is moved to OFF it mechanically closes a fuel shutoff valve on the FMM, thus ensuring the engine shut down
and
The metered fuel flow is sent through the FCOC to the fuel nozzles. The FMM include a Fuel Metering Valve (FMV) which, under the action of the Electronic Engine Control (EEC) (when the engine is in automatic mode) or the ECL (when the engine is in manual mode), sets the fuel flow over the full range of the engine operations. The FMM includes a Fuel Metering Valve (FMV) that is controlled by the Electronic Engine Control (EEC) or by the ECL to meter the fuel flow over the full range of the engine operation. Depending on the FMM mode of operation (AUTO or MANUAL), the Fuel Metering Valve uses different methods to meter the fuel flow: • in Automatic mode the EEC commands a torque motor • in Manual mode the ECL moves mechanically.
Brutal - I suspect you are correct that a double EEC failure was not considered likely or probable and there are more than enough boxes to be ticked on a check ride without adding that one.
Pretty much every annual Categorisation Check I did on RAF Sea King pilots (30 pilots/year for about 12 years) included dealing with double manual in the aircraft. It was a very uncommon emergency to get for real (although I know of a couple of instances) but we trained for it regularly.