Derailleur indexing problem - doesn't change from 8 to 7 but skips form 3 to 1 I just fitted a new 8 speed Shimano cassette (CS-HG41-8) and chain (CN-HG40) to my new turbo trainer (Elite Suito). Answers to my previous question suggest that this should work OK (see Can I put a 8 speed bike on a Elite Suito 11 speed direct drive turbo trainer).
The fitting seemed to go according to plan (fitted 2 spacers=1.85mm in total on the trainer's freehub, then the 8 speed sprocket cassette, then the lock ring, then left and right chainstay adapters as required for 135mm dropout spacing, then installed the bike using the quick release and dropout adapter supplied with the turbo trainer). I then indexed the derailleur by setting the high and low limters then tensioning the shifter cable and adjusting it according to the instructions in this YouTube video: 
                
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If I adjust the shifter cable tension using the barrel adjuster to get a nice, clean gear change from the highest (8th) gear/sprocket down to the next one then the gears shift cleanly down through 8, 7, 6, 5, 4 but when I shift to 3 the chain skips straight over to 1st gear without engaging 2nd gear. If I reduce the shifter cable tension a little bit then the gears shift cleanly down through the low gears (3,2,1) but there then doesn't seem to be enough tension to shift down through the highest gears (nothing happens when I click the shifter from 8 to 7 and the chain only shifts down when I select 6th gear). I can't seem to find any setup that works at both ends of the gear range. I don't understand how the shifter cable tension can be correct for the gears at one end of the range but incorrect for the other end of the range. It's almost as if the increments produced by the shifter are not quite compatible with the those required by the cassette but shouldn't a Shimano 8 speed cassette work with any Shimano 8 speed shifter? I also checked the rear derailleur hanger isn't bent - it seems fine as far as I can see and I think it worked OK with the old cassette and chain that were on the bike before I repurposed it to use with the turbo trainer. Any ideas where I'm going wrong are gratefully received as I'm basically following instructions here without any huge insight into what I'm doing!
Thanks in advance.
Good description of the problem, I think you've done everything correctly so far and the issue you describe is normally a misaligned derailleur hanger. It doesn't take a lot of misalignment to cause this issue.

I don't understand how the shifter cable tension can be correct for the gears at one end of the range but incorrect for the other end of the range.

You're right, it normally shouldn't because the 8 speed shifter will pull exactly the right amount of cable for the derailleur - shimano 8 speed will always work with Shimano 8 speed. If the gears behave at one end of the cassette they should behave at the other end. Whenever I work on a bike and have this trouble I think 'derailleur hanger' and proceed to straighten it.
You straighten a derailleur hanger with a specific hanger alignment tool, which references the wheel rim itself. A difference of +5 mm at one side of the rim and -5 mm at the opposite side can give problems with shifting like you describe; for a diameter of 622 mm this is a very small bend of the hanger.
Normally this is a rare enough job to pop into the bike shop for a quick adjustment, not least because you will take even greater care not to bend the hanger in future. During a pandemic you can do your own cost/benefit.
As long as the limit screws are set properly, this problem is mostly a bit annoying rather than dangerous. You might find an indexing setting where it's a bit sluggish to go into an easier gear on a certain sprocket, but an extra half push of the lever encourages it all the way on. That's a valuable skill if you don't already do so, but reliable indexing obviously preferred.
Here's a photo of such a tool in action for your reference (it's not a link (!) though videos exist of course)