Ok, ok. Good points. I guess I thought since I had seen some other posts about switching ground to provide power to a system, I could choose to do that, but I understand now from your post that perhaps that's only an option when you only have a single power source, and you are switching ground, but ground is still shared and common for all elements of the circuit at all times.
I changed my schematic above and last night so the 7.5V was connected to common on the switch. In increased my regulator to output 9V DC, (the lights take 5.5V -> 9V DC) I put a voltage divider on both NC and NO and set the resistance so they'd both output about 4.9V DC and connected them to digital pins in pinMode INPUT.
I left the diode in, and measure the voltage at Vin both with the lights all on and all off, and it never dipped below 7V, so I don't suspect the problem about instability in the Arduino regulator is the issue.
Here is an updated view of the changes I made to address Mike's comments:
Changes
I am thinking of using the switch to control a relay to connect the external voltage to the lights and Vin, so I have a cleaner digital on/off indication.
Despite all these changes, I still have flicker.
I've tried putting caps across the power to the lights.
I'm going to try:
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writing a sketch that just turns the lights on and off and see if I get flicker powering the Arduino and lights completely off the external supply. The flicker seems to be somehow related to providing power at Vin. Sometimes plugging the external voltage in an Vin completely eliminates the flicker, sometimes not.
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Seeing if somehow the lights are getting to hot: reduce current? Add a fan?
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Buy a new power supply instead of using wall wart to buck converter. Maybe this: 12V 5A switching power supply : ID 352 : $24.95 : Adafruit Industries, Unique & fun DIY electronics and kits
Anything else you guys can think to try? Reminder, these are Macetech Megabrites