Another question about current sense

Current sensing is P/O local control. Cutting the jumper disables Local Control but does not stop the current leakage through the load to detect the local switch changing state. The leakage is what keeps LED bulbs lit and CFL bulbs flickering. On older modules cutting the diode stopped the leakage current (and by default Local Control) but I do not know if this still works on newer modules. I think Ido's information is still the best around.

Technically one mod, the jumer cut, defeats Local Control. The other mod, the diode cut, stops the leakage current. However if you cut the diode but not the jumper on pin 7 of the chip, pin 7 (a high impedance input) remains connected to a half dozen components, which are now electrically "floating". That doesn't make "happy time" for the pin 7 input. Some modules become unstable. Some may work fine.

I guess I should verify what "local control" means. Does it mean if the module was plugged into a switchable wall outlet. Vs - current sense allows you to turn on the applicance/light from the appliance's built-in switch?

Local Control IS the capability of controlling the light / appliance at the units switch. Current sensing through the load is the way "local control" senses the table lamp / appliance has been turned OFF-then back ON for the local control function.

Plugging an X10 module into a switched wall outlet is redundant. Doesn't make much sense to do it unless you leave the switch to the outlet ON all the time. If you are asking if a module will turn ON when the switch controlling the outlet the module is plugged in to is turned ON, the answer is no.