Voltage at fixture after disconnecting switch leg

How much does the driver itself use? the driver has some level of impedance in converting the AC to DC for the LED. Question is, Is 6 volts enough to cause perceptible light from the LED and give even 1-6 V DC when you drop the AC source from the nominal 120V AC to 6 volt AC?
Good question.
In the case of a low end LED night light replacement lamp vs an incandescent in our personal bath vent/light the voltage was well under 6 volt. Apples to oranges comparison for sure
 
It takes under a microamp to make a bare neon or the most basic of L.E.D. type circuit produce light that is visible in the darkness.
In the past, it was common back when L.E.D. lamp bulbs started to hit the shelves. When you pair it with a solid state motion activated switch, the slightest of the leakage current was enough to cause them to do a faint glow, and sometimes cause the bulk storage capacitor in the LED ballast to slowly build up and cause it to flash at some interval.

Modern LED lamps have the LED ballast designed in such a way that a microamp level current flowing through the socket won't pass through the LED elements themselves to prevent the nuisance glow.

Try checking the hot and neutral wires at the fixture using non-contact voltmeter. If the open circuit voltage is truly a few volts, it won't trigger. If it's near line voltage, it will notice. You're only seeing six volt, because the 10 MOhm input of the meter is enough to pull it down to that level.
I think you might underestimate the powerful lure of higher profits from cheap designs on LED lamps… Eliminating a 10 cent resistor on 10 million lamps nets them $1 million.
 
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