That is an archaic indexing system from what I am able to tell.
Unless you have empirical data, you're not going to find that number with standard "inch" mini bike tire numbering on new tires, as height is not part of the "inch" indexing system. Most of the Chinese tires (Chen Shin) on 6" wheels are at 12" or slightly taller, and the 530 X 450 X 6 tires OldMiniBikes sells are around 14". (Includes the Coker which is an excellent tire)
The metric system of numbering tires does include aspect ratio, where the aspect ratio is a percentage of tire height based on nominal section width. For example, a six inch based tire with a width of 4.5 inches would have to have an aspect ratio of 70 to get you to 12.3 inches.
Calculator Here. The aspect ratio is the second number. (After the slash)
Most of the six-inch metric tires seem to be in the 145/70 size, and that is nearly 14" tall.
There are two used tires listed as 12.5 X 6 that have been on Ebay for awhile that don't look too bad, and are unique. Old is mostly for show though.
There just aren't many choices for tires anymore.