Why does a dielectric liquid need to immerse the parallel plates in a conductivity cell?
R134a is also known as Tetrafluoroethane (CF3CH2F) is used as a refrigerant, film propellant and many other applications, evidently here as a voltaic cell.

Being an insulator, it has all the properties of a dielectric.  the conductance of ionic contaminants is a highly variable parameter since the ppb or ppm levels of contamination greatly affect the charge flow in the medium when exposed to a DC or low frequency AC high E field.  The dielectric breakdown levels are significantly reduced by these impurities and the events called Partial Discharge (PD) have enough energy to breakdown the ionized particles surrounded by an HCF molecule cause separation of these molecules releasing Hydrogen as one of the components.  

The Lower Explosive Limit, LEL for such a concentration of H2 in the inert gas or fluid may be somewhere above 4% as it is for Transformer Oil, which is the level of removing an oil filled transformer from service to reduce the risk of  explosions. Thus filling the void space with an inert gas such as Nitrogen is commonly used.   

Perhaps reducing the volume of N2 in the enclosure allows the vapour pressure to rise to inhibit the release of H2 in the fluid which can absorb a much higher volume mass of H2 and these minimize the H2 concentration level in N2.

A Teflon seal that allows only H2 to pass, is often used in outdoor sealed enclosures with SLA rechargeable batteries to release the pressure of H2 during charging.

In the end, the measure of conductivity due to capacitance by rate of change of the applied current will be constant except for some slight thermal variance. The capacitance May be easily measured and current computed by \$I_c=CdV/dt\$. But it is the ionic conductance that is important that is a measure of the impurity from contaminants. Thus a slow ramping DC is necessary for the measurement.

PD can easily be detected with a high speed DSO and probe wire shorted with few turns around the electrode wire fed into 50 Ohm coax and terminated with a 50 Ohm Load, or heard on a quiet channel on an AM radio like a lightning tick, hundreds of miles away.  the rise time will be less than 1ns so the faster the DSO, the larger the amplitude of the current pulse. PD is often calibrated in pC but can also be measured in Watts for the duration of the discharge in [ns]. A slower scope will just reduce the amplitude and stretch out the event,

When the flow of ions does not have enough kinetic energy to ionize and create release electrons abruptly, it just circulates in the conductor and back thru the dielectric. This is the current you want to measure.  The PD is reduced by electrode smooth surfaces and may be affected by sharp edges of the plates where contamination may accumulate.  However a battery ESR is greatly improved (lower) by micro surface roughness from acid etch or similar process.

It should not be affected by heat or current as much as the small gap which increases the battery capacity and the contamination Level on PD rate which increases with reducing gaps. It is akin to a Relaxation Oscillator like a Unijunctuon. 

However the PD energy level increases with gaps as the distance for contaminants to be accelerated and “detonate” from impact, releases more PD energy. 

Thus there are many tradeoffs in such a design and contaminant filtering/processing is the ultimate challenge.

Final word

I don’t expect any PD at 1kV in your gap but if you ramp up slowly to the 1st PD event (1 pulse per minute) this is known as the PDIV ( Inception Level) and is a measure of the margin before breakdown voltage . (BDV)  In a Battery this is more serious as there is a voltage source that will sustain current above then holding current unless some reverse pulse current is applied. this behaves like a latched SCR until current flow drops below holding current levels. I imagine if H2 is generated rapidly, there needs to be an escape pressure valve just as there is for transformers.

In transformer oil testers with a 2mm smooth gap, it is rated for >25kV and when further refined to remove all moisture and particles is capable of 75kV. But defective contaminated oil will fail with PD well below 25kV before it breaks down.