PDLC Electrochromatic Film / Switchable Glass
Regarding the operating voltage, it looks like these "switchable glass" devices work similarly to LCD's and will require an AC drive voltage to prevent damage over time.

Smart glass handbook (Courtesy of google)

http://www.smartglassinternational.com/downloads/LC_SmartGlass_Handbook.pdf

As to what the frequency of this voltage has to be I have no idea, assuming a transformer in your ebay link, around 50/60 Hz. 

An EL wire inverter (ebay link below) claims to put out >100V AC so may be too much voltage to use directly.
Also the output frequency is not stated, but el wire apparently works between 400 &amp; 2000 Hz so is probably somewhere in that range. This may or may not be suitable. 

To make it adjustable you might be able to vary the input voltage with something like a buck/boost converter module (assuming the inverter has no regulation)

This is much easier than regulating AC

Note that varying input voltage may also vary the output frequency of the inverter!  

Buck/boost converter module:

https://www.ebay.com/itm/Boost-Buck-DC-adjustable-step-up-down-Converter-XL6009-Module-Voltage-NEW/191673952440?epid=911606552&amp;hash=item2ca0a868b8:g:0CAAAOSwLVZVs4ch

Inverter module:

https://www.ebay.com/itm/Mini-DC12V-1-5M-EL-Wire-Cable-Neon-Glow-Strip-Light-Power-Driver-Inverter-New/182701362456?hash=item2a89d98d18:g:rLMAAOSwxDNZhBiM 

Basically:

1)You have to use AC, DC will damage it and probably wont even work

2)Not sure about exact drive voltage/Frequency... 

3)There are better solutions than the one above as its a bit of a hack

4) Ideally you would want to build a proper driver 

This ebay listing shows some of that PLDC film with what looks like a battery powered El wire driver so maybe higher frequencies will work? As to how good for the film this is im not sure...

https://www.ebay.com/itm/15X15cm-White-Smart-PDLC-Film-Switchable-Privacy-Glass-Electrochromic-Sample/282768238917?epid=11011203602&amp;hash=item41d64ce945:g:eqkAAOSwWclZeuJW

Also, the power required will vary depending on the amount of film you are going to be driving.

As for dimming, I don't think this film is fast enough in terms of switching times. You would likely end up with nasty strobing effects.

Dimming in AC tends to require chopping up the waveform with something like a triac.