LED Spotlight array issues
Ned, the individual lights are spec'd to accept a wide voltage range (9-32 VDC), so there's obviously a driver circuit in each of them. The driver rapidly turns the light on and off, much faster than you can see, to regulate the average power dissipated by the LEDs regardless of the different input voltages.
This means the actual current draw varies between some peak value, and near zero, hundreds or thousands of times a second. You could see it with an oscilloscope, but it's not detectible by the naked eye looking at the lights.
There is no synchronization between your multiple light units, so when you connect multiple lights in parallel, it's unpredictable how those waveforms will combine. This will create a complex waveform of current draw. You could get huge peak currents far beyond the specified average current. It could also interact with your power supply to trigger current limiting. And finally, your ammeter may not be able to accurately read the average current of a complex waveform.
You may be able to get away with wiring sizes that assume the spec'd average current draw is correct and ignore your meter. But I think that's dangerous. Can you find a friend with an oscilloscope?