On the older model Appliance Modules. There is both the Local Control Sensing circuit and the On/Off status of the module sensing circuit.
If you did the Local Control modification. The very small ratchet switch On/Off sensing circuit is still there and it can not be removed. If you do it will not know if it is On or Off and pulse a few times like a machine gun.
The newer CFL friendly appliance modules have no Local Control Sensing circuit so there is no modification to do. The On/Off sensing is still there. You may want to try a small incandescent night light or other very small load. On the output of the appliance module and see if it helps.
Unless the present appliance modules went to a new design with no ratchet switch. Like a real relay. It is probably still there.
The only other brand module I have seen. Was the Insteon 2635-222 On/Off module. It has no Local Control Sensing or any current I can measure on the output when Off. The earlier hardware revisions still could accept an X10 address programmed into them. The present hardware revision may not accept an X10 address. As they officially dropped X10 a few years ago but unofficially some modules still did. The older 2456S3 ApplianceLinc. Has Local Control Sensing but if you where real good with surface mounted parts removal. They could also have Local Control Sensing removed.