"...what in your schematic now activates the warning light?"

That's easy. T3 is forward biased through R4 and supplies a return for the failure indicator at K. But that's the 1362367 sensor used in the late 240. I have no idea what's in your car.

"So, I ask, why is our bulb sensor design seemingly more sensitive with lower current LEDs?

Again, can't say about the 940, but your one-third two-thirds hypothesis was certainly interesting. Part number?

As to reed switch pull-in current, that depends on the number of turns and current, which for the 240's circuit I do know, is matched to the expected load. If not enough load is present, because of the LED's reduced demand, the reed switch won't close.
--
Art Benstein near Baltimore