from ambient RF" I tried several different types of diodes and Ferrite rods and coils and could never get a measurable voltage across a .01 uf cap.
I don't see how you can make this work short of driving a micro Telsa transformer and prayer. There just isn't enough total power except very close to the transmitter or voltage available even in the tuned circuit tank and as soon as you try to draw any current the Q falls rapidly.
You have to get to about 80v for a neon lamp to break down and glow. By comparison getting 2-3v at 0.1uA or less for a white LED to just start glowing should be a lot easier but still a bit of a challenge.
A high long wire antenna isolated from ground will quite often have enough DC potential at very low current to light a neon screwdriver just from the atmospheric potential gradient. Uselessly low current except during thunderstorms when the LED would be at risk of damage.
My TV aerial is high enough up that on most winter days it will light a neon screwdriver at ground level! A book value atmospheric gradient of
100V/m is typical but some days it is much more and at high enough current to notice. If you try to measure it with an ordinary DVM rather than an ultrahigh impedance electrometer you tend to get much less.I would expect it to be able to provide enough current to light one of the more sensitive LEDs provided it was protected from the overvoltage. Never tried it though.
You can drive electrostatic toys from the potential difference across two decent sized plates at different heights in the same way as with a Zamboni pile like the perpetual ringing clock in Oxford.
A simple variant also serves as a thunderstorm alarm.