Two lights function intermittently

1. My stairway lights are wired through the ground fault circuit in one of our bathrooms. This summer, the GF started tripping when the stairway lights were turned on. THis is an intermittent problem, and only occurs when the humidity in the house exceeds 50%. I replaced the GFCI outlet, but the results are the same. Since this is a humidity associated problem, would I be ok in removing the lights from the GFCI protection since tehy are not in wet areas or should I investigate further to see if there is a nick in a line?
2. My security light outside is also functioning intermittently. Last year the light started to go out at times. This summer it did not fucntion at all, but we did not miss it. As the sun set earlier, I decided to look at the light. I removed the cover, cleaned out the housing and replaced the sodium vapor bulb. The light still did not function. The light will come on when it is dark and the outside temperature is below 40 degrees. If the temp remains above 40, the light will not come on. I checked connections and they all seem good. My only other thought was a failing light sensor, but being temperature dependent seems a little odd.
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The stair lights don't need to be on the GFCI circuit and you may be able to disconnect it at the outlet location, which you would do by removing the wires from the load side of the outlet and pigtailing them on to the line side. The thing you have to be careful of is that there aren't other bathroom, unfinished basement or outside outlets also attached to that GFCI.

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I suggest changing the photocell, ballast, ignitor, and the capacitor.
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