tweaking the switch may just set somthing off further down the line, so it could be a relay that you sorta kick into working by messing with the switch a little.... and i'll say what i always say during electrical problems like this...
check your grounds.
(tho that answer most likely wont apply here)
i figure that it could be somthing thats so corroded that the expansion and contraction of heat/cold can actually cause it to work or not due to how little of the conductor is left.

it could also be yor battery, i mean it sounds like it might be dying on you, the headlights pull more than the parking lights and well, if everything works fine after the alternator kicks in for a while... i'd say it is your battery

there are a million little things that could effect that... so it's hard to say without diags or even just being there to see the car and whats happening