first of all I think that "more known for it gears and accuracy at the fast/high spin level" could use some more detailed discussion.
lets try to discuss in good faith. To answer your questions broken ball:
1. what is a gears?
a "gear" is terminology for the range of speed a paddle, rubber, or blade has. You can specify the type of stroke tested, but most people assume a loop I think. "high gears" means the equipment has the ability to produce slow and fast loop; you have the ability to control the parameters of the loop. "low gears" means only slow or only fast, with less control over the range.
For blades, a carbon blade like Primorac would have less gears as it has a higher minimum speed. Beginner allwood blades also have low gears as there is a limit to top speed. Innercarbon blades generally has wider range, allowing slow and fast depending on how hard you hit the ball.
For rubbers, less to no sponge have the least gears. For standard max sponge inverted rubbers, soft sponge has low gears as they have a max cap on speed. Harder sponges allow higher max speed, thus having higher gears. Rubbers with more reactive sponges or like Tenergy or most "euro" sponges with tensioned non tacky topsheet have higher base speed, thus having lower gears. Tacky rubbers, even boosted, generally have less gears with more control over low or high speed shots.
I don't know the history of the term, but I suppose it is derived from the rear cassette ("gears") on a bike? or maybe gears in a car.
How many does H3 have vs T05?
2. "gears" is a relative term (rubber A vs rubber B) and subjective. There may be a measurable value to directly describe gears, perhaps... As having tested both on a specific blade with my specific technique, T05 seems to have less a higher minimum speed. Boosted H3 has a lower minimum speed, but can have a very high topspeed. (I don't remember topspeed of both compared to each other). So yes, it seems H3 to have more gears than T05.
Now, just saying "H3 has more gears than T05" is not that useful, its more useful to describe the details of how the rubbers work for you, etc.
How does one shift gears?
3. I don't think "shifting gears" is a term used. You just use the term to describe a piece of equipment in discourse. (X has high gears or higher gears than Y.)
4. Does the Tieffenbacher pdf mention gears?
Epar might give an indication toward the gears of a rubber or blade. For example, marble has high Epar at low velocity, suggesting high minimum speed and lower gears. Allround have lower Epar at low velocity. suggesting higher gears than marble. It is also later mentioned that sticky rubbers lower Epar, as expected, and may allow lower minimum speed and thus higher gears. But, there are several other factors in stroke mechanic that might influence a persons perceptions of the "gears" of a piece of equipment, so the relationship is to be explored more (beyond my level of prediction.)
5. How is one rubber more accurate than another?
Maybe Tony is saying that H3 is more comfortable for counterlooping ("fast/high spin level"), or for dealing with more spin in general? I certainly can say I do prefer sticky rubber for countering incoming high spin balls, whether slow or fast.