This might be happening because the load sensing works by supplying a low voltage and detecting leakage current while the CFL presents a diode-capacitor load which only pulls a short spike when initially connected to a low voltage and doesn't pull serious current unless the voltage is high enough to make the oscilator start and the lamp to light and pull a load.
You might want to try putting a 48K 2W resistor across one of the lamps (or put it in a plug and plug it into the wall when only one lamp is turned on as a test) to see if that makes the inverter start. It will pull one watt at full power and nonzero current at a low DC voltage.
Or a 7W incandescent night light is guaranteed to do the trick (presuming the switch labeling is accurate), though it seems a shame to pull half the lamp's power just to make it start.
If that works here's a thought: Get one of those incandescent night lights with the photosensor and hook it in parallel with the lamp, with the sensor near the lamp.
When you turn it on (if the room is dark):
- The night light will come on,
- pulling enough power to start the inverter,
- lighting the main lamp
- which will give enough light to turn the night light off,
- dropping the nightlight's consumption to leakage power only and leaving you
effectively with only the CFL.
Of course if the CFL doesn't draw enough power to keep the inverter happy even after it's running, the inverter will shut down, which will shut down the lamp, which will light the night light, and the whole business will blink. B-)
