The lights were on in the middle of the day within a few hours. So I guess the signal to turn on is not RF generated and is due to "noise" coming down the power line or from some "offending" appliance or light. I don't know what I can do about that.
$0.02
In another home, I had two high pressure sodium lights on the garage which ignited similar to your description of your "iodide" lights. My lights had a temperature controlled starter circuit that would trigger the "local sense" circuit in my wired in Appliance Module which controlled the lights. This might be your problem, although you seem to have a random delay where my would kick back on about 10 minutes after they were turned off, and if I understand, it is a new problem for you in an old installation.
You can search "local sense" or "local control" for more information. Older Appliance Modules can be easily hacked to disable the circuit (but the newer Appliance modules have been redesigned, and the hack will not work on them. No way to know where your XPFM are with out opening and looking at circuit board. If the controller chip is on the solder side of the PC board, you have the newer model.
That said, there is another hack which basically puts another load across the XPFM so it will not "see" a starter contact switch taking place in the load. Is there a way you could temporarily wire a an additional incandescent light (say 40W ) across the output of the XPFM and see if the lights come on unexpectedly with this "blindfold" in the circuit. If they do not, then at least you know what is causing the problem.
If an Appliance Module it is easy to use a "cube tap" to also plug a 7W night light in the circuit which works. A 33K ohm 3 watt or greater resistor may also make you XPFM blind.