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Glen, you know I read anything you write. Might just be too late to be of any help, but this time, between you and Bruce, I find myself laughing at your mention of my name. Then, the Dan Rather analogy has me in stitches.
Here's my guess on the workings. The sensor works by surrounding a magnetic reed switch with two coils of wire wound separately but connected to the left and right lamps with opposite polarity so equal currents will cancel the magnetic field around the reed.
When the currents become slightly different, enough field is made to pull the iron insides of the reed switch into contact, but inside, it is arranged to latch (magnetically), or hold the contacts together with a smaller field than needed to make the contact initially. This prevents contact bounce.
If the unbalance is on the "hairy edge" of what is necessary to light the warning light, the effect of that hysteresis or latching is to have the warning either fully on or off, not dim, or flickering, so you might start the car twenty times with the same lamp problem, but only get the warning lamp ten of those times. Same effect your home heating thermostat uses.
Also, changing the current being drawn in the front parking lamps by a large amount, as would happen running the 25W filament instead of the 5W, because of the real resistances in the fuse and contacts, would affect the voltage available to the taillamps through the current sensor. Less voltage to one circuit would would make the same taillight load imbalance tip the scales - reducing or increasing the field around the reed switch, depending on whether it aids or bucks the load difference.
The one remaining factor in the bulb out warning is only important in dry climates at low altitude. The Volvo designed finooken valve piston seals shrink with low internal pressure causing false activation of the muffler bearing service indicator circuit, sometimes disabled by the do-it-yourselfer to prevent excess nylon gear stress on higher mileage cars.
Hope this helps as you feared, Glen.
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