Ok are you using the powder KOH?
Did you have the coil in series or parallel or none at all just the DC power?
With straight DC the current is the V / DC resistance across the anodes.
The closed you get the lower the resistance 3mm should be as close as you need with this or even 5mm.
Your cell it acting like a very leaky capacitor, that is normal with using KOH.
Series Resonance with the coil in series with the leaky cell is at resonance as you know is
XL = XC then DC resistance of the coil and of the cell at resonance is all that the circuit will see.
With the coil in parallel then that now is a new ball game, it is still the same at resonance the DC resistance is then like two resistors in parallel.
Now if you have then a DC 50/50 pulse, when the pulse drops to zero some of the coil charge will discharge how much will depend on how quick the disconnection is.
Then the cell will discharge into the coil, until the voltage it is lower than that of the cell and so on until both are discharged.
If the set frequency is high enough at resonance so that the coil does not even get to the T constant it take 5 x T to reach full current.
You will still get the voltage across the cell, it still is the resistance in parallel but the coil discharge may all go in a small negative pulse so then you will have just the cell discharging the ringing is shorter.
You can then adjust the frequency and the resonant point to give you a high voltage the full say 12V with very little current and you then have the voltage doing the work.