In the automotive industry (american) we typically name the cable 1cc, 2cc, 3cc... for the "Control Cables" and 1mc, 2mc, 3mc for the "Motor Cables"
Then in the control drawings we identify the "Pin" number being used for the signal in the schmatics, and also...
You said you checked the "hots" remember the neutrals or grounds are just as important. If it is the feed to the house, everything in the house will dim at the same time, it did not sound like that is the case from the information given. It is more probable that there is a poor...
I thought I recentlly read about a VFD that had a built in micro-PLC built to control some local IO. I can't seem to find the article, but I have an appication where this combination would be a sweet solution.