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ozark01:
The logic of the lights with which you are working represent a sequential type of control, partly by time periods, and partly by stepping. It is a type of system I would never personally have. In my opinion a quite undesirable mode of operation. It is sort of like electronic clocks where I can only go forward to set time or alarm. I much prefer absolute address systems. However, this is not your problem.
I doubt you have a defective transformer. What would cause output stepping of the secondary voltage? Only the overload sensor in the transformer, and this is unlikely based on other positions of the MOV. There is no reason for the MOV to cause the problem either. I would suspect the LED lights, but have nothing to support this guess.
The GFCI is not an automatic resetting device and therefore should produce no output pulsations.
I would remove all load from the transformer secondary. Then determine how to prevent switching of the transformer primary from tripping the GFCI. Doing this with no secondary load, and with an incandescent full load.
Once this works, then use only the LED lights as the load. Do they act funny. If so, then I would classify the LEDs as having a defective design. Or wiring problems.
With the switch on steady, not turned off, do the lights change state.
Another possible experiment is to use a relay to switch the low voltage output of the transformer. Does this correct the problem?
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