You should be able to find the parts on ebay, but probably not that geared rod. There are even some reproduction parts sold, such as the scissor equalizer.
I've not seen that gear drive equalizer though. The scissors thing works, but the geared rod works better. I never looked up when they made any of it.
I picked up an early GW a few years ago. I'm not an expert but my understanding is they only made a scissor type equalizer, with different variations of it over the years.
To identify the slide and/or cabinet I would send the pic to a business that restores furniture antiques.