Welcome to the forums captainradon.
I will take you up on evaluating your idea.
First is the initial charge on the pails, if you start with both pails in the
same medium such as open air then what gives them their opposite
charge? If you precharge them they will equal each other in a short
time due to ionized air that is omnipresent.
In farradays water dropper experiment he used the initial
charge that is true but he built up the charge over time using water as
the dielectric because it is Bipolar and isolated from all the other water
dropplets thereby creating multiple charge carriers. Gravity is used as
the work function in that setup. Since I do not see any work being done
to maintain the pail charges then no gain will form.
Second is the capacitors. When you have a charged capacitor and
connect another that is discharged to it the energy will distribute itself
between the two. The capacity of the buckets is very small so when
you connect any other plate capacitor of larger value to them you will
not have enough power to align the molecules of the capacitors
dielectric between the plates.
The charge in a standard capacitor is held very tightly in place by
the dielectric field lines that close themselves between the plates
through the dielectric so that if you tried to short 1 plate of one capacitor
to another capacitors oppositely charged plate it will not release any
energy from either cap so the last diagram will not hold true of having q*2.
Last is the amount of work it will take to switch the capacitors
in and out of the circuits will far outweigh any gain of the system in its
current format.
Having said that, there are a few things that can be conveyed to help
you on your journey. If you truly want to make a motionless electrostatic
generator then there is no better example than a Tesla coil. If you want
to stay in the same framework as the dropper then you can only modify
certain characteristics of the setup and not its modus operandi. First
thing to figure out is what will you use as a charge carrier? what would
hold the most charge per weight, how many carriers can be moved, and
how fast can they be made to move from point A to point B.
Electrostatic induction from the water droplets falling through the
rings induces a charge of opposite polarity to the drops till they hit the
buckets and through electrostatic conduction they give the buckets the
same charge as the drops which in turn adds more charge to the
oppositely wired rings thereby continuing the cycle until you discharge
the buckets together neutralizing them and the process repeats itself.
A man named Robert Van de Graaff patented one of the first
Electrostatic generators based on the same concept as Farradays thunderstorm.
Here is another patent that uses the same concept.
If you want to discuss this any further or try another direction like
using moving charged plates near each creating voltage gain for
example, let me know.