Disconnecting a cylinder
 

Has anyone tried adding a switch or relay to one of the injectors to turn one cylinder off?

I think they kill power to all injectors usually if the vehicle didn't cone with variable cylinder deactivation.
The engine is going to run poorly and not get very good fuel mileage while trying to pump air through a dead cylinder.

One issue with only shutting down the injector is that air will continue to be pumped through the cylinder. This will result in the oxygen sensor in the exhaust reading lean. The engine management will then richen up all the cylinders in an attempt to achieve a stoichiometric air fuel ratio, resulting in poor fuel economy.

One method that might work would be to have a throttle for the intake runner of the deactivated cylinder. This throttle could be closed when in deactivation mode.

The automotive companies actually use valve deactivation.

Of just run all the cylinders lean.

My Fit had an injector go bad last fall. It was bad, I'd never do it on purpose.

My Saturn had its coil pack fail last winter and I drove it around for like 2-3 weeks... even with the injector disconnected on the non firing cylinder, my mileage dropped from
~42mpg to ~28... the issue was that it didn’t have enough power to handle pulse and glide, and it lacked power bad enough that going up hills that were normally doable in 5th gear, was then only doable in 3rd or 4th... the engine was really rough below 1800 RPM, so I also had to keep the revs up... that’s also not accounting for the richer AFR