Sounds like you're on the right path. The lower shift cable is the one that actually shifts the drive.via the shift actuator
There should NOT be enough force on the lower cable to cause the shift actuator (#37 below) to move far enough to actuate the switches when going into gear (or out of gear for that matter
if the drive is being shifted out of gear with the boat sitting on the trailer.....this also means that you cannot test for actual correct shift actuator operation unless you test it in the water. )
When in the water, there is sufficient holding force due to torque on the shift dogs .....so that the ESA provided torque (reduction) pulses , will allow the shift dogs to separate when the shift actuator moves far enough to actuate the switches. and it will since you provide the extra pull (or push) to the cable coming out of gear.
As indicated above, if the lower cable or mechanism in the drive is binding even a little bit, it will take extra force to shift into (and out of) gear. THe extra force is usually enough to move the actuator enough to actuate the switches. If this is happening, you need to either replace the cable and/or clean up and /or lubricate the mechanism Bruce was talking aobut