Are rear derailleur cable intervals equal? On one occasion in the past I paid attention to get the rear derailleur to be "just right". On eight gears on an MTB, I would get gears 1-2-3 and 5-6-7-8 to be perfect (minus the chain rub on one end or another, depending on the FD position), but I couldn't eliminate a nagging problem from gear 4. On occasion, the gear would shift back and forth between gears 4 and 5.

I'm now tuning a new bike, road this time, and would like to understand enough to never experience this again.

From "How to Adjust a Rear Derailleur – Limit Screws &amp; Indexing"  I pulled this image:



The image clearly shows that the distances moved by index shifting are not equal.

And so I'm now telling myself, perhaps my unsettled gear #4 was due to my having in the past pulled the cable too far in one direction or another. I was using the barrel adjuster to fine tune the derailleur under a cog, but the cable as a whole was misaligned. A picture will illustrate why this matters.



For some geometric reason, perhaps the misalignment didn't affect gears 1-3, 5-8, but affected gear 4.

Can this happen? I've never seen what's inside an index shifter. Will it happily shift beyond its range, stopped only by the limit screws?

As I no longer have that MTB, I don't really care at this time why gear #4 on that bike was sometimes unsettled. But I do want to understand:

Are rear derailleur cable intervals equal?

If the intervals are equal, then there is no issue. Shifting the cable cannot misalign the settings.

If the intervals are not equal, then something (the limit screws? the shifter? ...?) should stop the amateur mechanic from misaligning the entire cable.
Your assumption is that there is an unlimited number of clicks in the indexing inside a shifter. There aren't. For rear derailleurs shifters there is one click for each gear in the cassette. (i.e. a 10 spd shifter has 10 clicks). If you mis-align the clicks, you only get 9 gears not 10. 

Often the indexing is setup to pull a larger amount on the biggest cog ( or lowest gear) in the rear cassette. It's tuned by the manufacturer to get the best shifting performance based on the typical cassette used in the group. 

I suspect the issue from your older bike was not due to indexing, but due to a worn cog in the cassette. One gear in the middle just being flaky is a common symptom of a worn cassette and chain. 

Cogs don't get the same amount of use or force through the chain so they often wear at different rates, especially if you don't replace your chain often enough. If you want the best shifting, get a chain gauge and check your chain for wear at regular intervals. My strategy is to buy the cheapest chain that works and replace it often.