Trying to find out why operation is erratic, I measured the voltage across the hard-wired pushbutton in the garage.
The button is illuminated by a red LED, which is in series with a 1k resistor across the switch. The LED is always on. Pressing the switch shorts the resistor-LED pair and operates the door.
The puzzle is that when I disconnect the LED-switch assembly and measure the voltage across the wires from the opener unit, I get only a couple hundred millivolts DC, and less AC.
How is it possible for the LED to light with only 200 mV across it?