As I'm sure you know now, vinyl tiles are even less shiny when new than cheap ceramics and don't have the baked-on glazing ceramics do, neither are they are as hard. Compared to ceramic, they're soft and often made to absorb the repeated 'shocks' of footprints. Trouble is, also they're cheap cost-wise too and therefore have a huge market share. A good installation - just like ceramic - goes a long way in how the ultimate floor 'looks" once installed.
On the other hand their surface is tailor-made for an acrylic liquid wax, as opposed to a paste wax that goes on thicker. It's not a coincidence that many companies - for example: Armstrong - make both tile and 'wax' to make them shine (because normally the unwaxed tiles don't). Acrylic floor waxes are easy to make and therefore many people make them.
The paste wax you may have used in the Army was based on buffable softer waxes that shine a lot more, and given the availability of cheap labour, was buffed a lot...and therefore looked pretty good.
As for acrylics, NCL's s "ONE" is a good one, but there are several others out there; you're not going to find much new under the sun in acrylic wax technology... still, each manufacturer will have their own way of applying it. That may be just as important as the product itself, so just get hold of one and apply according to the instructions.
Like stone polishing, the ultimate shine on a surface has a lot to do with the underlying preparation done to the floor. So, stripping and cleaning the floor prior to waxing is a big part of how the waxing process goes. The word 'clarity' springs to mind, as a 'clear' shine has most to do with the preparation of the subsurface than it has to do with the final surface. All has to do with light reflection.
It"ll never look like a highly polished marble floor...but didn't cost that in the first place.:wink: