Presumably you have tested the water flow without the shower head attached? Gainsborough shower heads will give the appearance of a trickle flow when the rubber nozzle plate distorts.
This image shows my original downstairs lighting circuit (after the upstairs was rewired to a separate mcb) which includes a bit of old style (1970's) two way switching. Maybe it can be of use to someone.
Never seen it done but just an idea.. :idea:
Another possibility if extending from a double socket and you have a problem joining in would be to replace your back box with a dual accessory box. Then use two single sockets in that box. The cables from the existing ring are then connected one to...