A pair of brake sensors with LED indicators arrived and should improve the situation on Mary’s bike.
The connector pinout, as seen looking into the jack on the controller side of the cable:

Of course, one cannot depend on color codes, but now we know it uses a 5 V supply. Some rummaging produced a suitable (“Julet”) connector, a cutoff USB cable, and a USB power supply:

You’ll note the sensor’s signal wire is blue, not white, but red = 5 VDC and black = common on both sides of the splice. This is not to be sniffed at.
With the disk magnet (supplied with the sensors) oriented edgewise to the sensor, so the magnetic field is largely cancelled, the maximum separation allowing the sensor to remain On is about 7 mm:

The minimum distance allowing it to be Off is 8 mm:

Orienting the disk face-on to the sensor increases the distances, because the magnetic field is not cancelled out in that direction. Similarly, positioning the magnet either above or below the plane of the sensor changes the results.
The maximum On distance is now 20 mm:

The minimum Off distance is 22 mm:

The other magnet has a similar field strength and the other sensor responds at nearly the same distances, so they’re reasonably matched.
The LEDs are, however, not well matched: one sensor is much brighter than the other. I only have one connector, so I cannot show both in the same picture. These pictures have the same exposure (1/120 s and f/1.7), with the top sensor appearing in the previous pictures:

The red LEDs show a similar difference. I’m certain this doesn’t rise to the level of a warranty claim, because, hey, maybe the brighter one should be dimmer.
Now, to fit them on Mary’s bike …
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