A couple of thoughts come to mind:
AFAIK, mines used a wide variety of gauges, depending on purpose, finances, era, and loads. Transportation was needed for both tailings and ore from a bored mine shaft, and transport of shoring materials, machinery, and ventilation equipment into the mine. This assumes the run from the surface to the vertical mine shaft was horizontal enough to use a tram in the first place. In larger mines, horizontal shafts on different levels linked by elevators were seen as the most efficient way to remove ore and tailings. Where horizontal shafts and elevators were too expensive, a tram on a slope powered by cables and winches would be the most likely solution. But even the latter requires the infrastructure to power the winches.
A small mine worked by just a few people in the 19th Century might use a hand pulled tram on 12" gauge, if they used anything at all. Your 18" gauge would be a good fit for a human-sized tram, as shafts would be minimum size to fit their human miners. A large production shaft mine of the 20th Century would probably have electric trams, and could be up to standard gauge in size to accommodate the considerable transportation needs of the large operation.
I have heard of mine trams using 12", 15", 18", 20", and 24" gauges, and a look at mining supply catalogs reveals more than the one gauge. If the mine can financially support the infrastructure of electric tram motors, they would probably have greater transportation needs, and gauges smaller than 15" become impractical. I'm not an expert, but I would think a horse- or mule-pulled tram would not be less than 2ft gauge to accommodate the animal walking on planks between the rails. And normally using the animal outside the rails would make the shaft unnecessarily wide.
External mining supply railroads varied in gauge in the 19th Century, too. The Gilpin Tram here in Colorado was 2ft gauge, and there were many 3ft gauge as well as standard gauge lines.
From the modeling point of view, the big question is whether the mine tram is a dummy, or is going to use powered vehicles. For powered vehicles, gauge choices are limited to availability of commercial mechanisms, unless you intend to scratchbuild the mechanism itself.
For a dummy tram, or one externally animated, gauge choice is up to you as long as you are willing to hand lay the track and scratch the vehicles. In N scale, a difference in 3" in track gauge is less than 0.5mm. That is getting close to the limit of my working tolerances (which is why I am in HO :mrgreen

. I would think - could be very wrong - that as long as the mine tram is less than 1/2 of standard gauge track wide, the appearance would have the desired effect. Again, the effect would depend on period modeled and the figures placed around/beside the tram, which would give it a sense of scale.
The point of the links I provided was to show that handlaying track for a mine tram in N scale was practical and feasible. To find out that commercial 4.5mm gauge mechanisms exist is an unexpected bonus.
my thoughts, your choices