The strip is exactly as I expected, but I did omit mention of the fact there are multiple sections in parallel. Functionally, it makes no difference when the strip is viewed as a two-terminal circuit. It could be three big LEDs and one big resistor or a whole bunch of paralleled segments.

But the configuration is not what you described...so how can it be “exactly” what you expected.

6 volts across 3 white LEDs simply isn't going to produce enough current hence light to be seen in anything other than pretty much total darkness. You might get a few photons per fortnight. If 6 volts produces dimmed but significant light, the controller is PWM.

Yes 6 volts across the leds will light them but they will be dim.

Simple ON-OFF PWM control is the only method that is broadly applicable and will perform in a predictable fashion without knowing the characteristics of the connected LEDs. It will work with white LEDs in triples with a resistor per triple or red LEDs with one resistor per LED or anything in between - as long as they are "dumb" LEDs. It will work for a current requirement of 10 A (if it could handle that) or 10 mA. It can work open-loop, though it could be made to limit the maximum average output to 12 volts, which would have some advantage for automotive use. Where it won't work is downstream of a switchmode constant current driver - the PWM would work but the CC driver would lose its mind.

No one is debating that

 

I'm sorry, I saw what I was thinking instead of what was drawn.

Yes, a resistor with three paralleled LEDs would certainly light at 6 volts. It will also be horrendously inefficient on 12 volts since 3/4 of the input power will go into the resistors, unless what is represented as individual LEDs are actually multiple chips in series, in which case we are back to dubious behavior at 6 volts. I really doubt the configuration is as shown. It makes remarkably little sense and is contrary to the arrangement used in every LED strip I've ever looked at. Current sharing among three paralleled single-chip LEDs that are not isothermal is going to be poor initially and get worse. The LED with the lowest forward voltage will hog more than its share of current, heat up more, reducing its forward voltage even more.

 

I'm back to being completely convinced that the rope light in question uses sections with multiples of {(three LEDs in series) in series with a resistor}.

The claim is 280 lumens for 3.6 W of input power at 12 V. That fits fairly well with 1/4 of the input power in the resistors (3 x 3 V LEDs in series), leaving 2.7 W for the LEDs and hence requiring LEDs producing a bit over 100 lumens per watt which is not state of the art but quite realistic. If 3/4 of the power were wasted in the resistors, that would leave 0.9 W for the LEDs, requiring LEDs producing 311 lumens per watt - slightly more than the theoretical maximum efficacy for LEDs. Nope! Not even if they are exaggerating the light output by a factor of 2.

The specified supply voltage range is 9 to 14.2. This may be nothing more than trying to fit the spec to reasonably expected automotive voltage, but at 14.2 V with 3 V LEDs, almost 79 percent of input power would go into the resistors if there were one resistor in series with (any number of paralleled white LEDs). Again, Nope! 9 V as a minimum is consistent with expecting a little light at the minimum.