My bike is a 2 year old, less than average mileage, 18 speed tension grip (not Shimano) shift type, dual spring and was never a problem. In a moment of madness I decided to make it an index shift and was informed that by changing the right hand grip it would become an index shift.
The grip shift is a Shimano index type but the other parts are not. Now I can only fine tune it so far. 1 - 6 will give me all 6 gears. When I go from 6 to 1, I only get 6, 4, 2 and 1.
I have tried everything; adjusting stops; re-tensioning cable; another grip shift; grease cables; fine adjust thumb screw; take it to Halfords; take apart 6 speed cassette and change ball bearings.
I have also noticed a play on the cassette when free wheeling but the experts tell me that it is normal. I have not noticed it on other bikes.
Any suggestions would be welcome. My options are to go back to tension shift or change component by component until (if ever) I get it right, starting with the cassette and chain and finally the rear derailleur
It sounds like you have an inexpensive freewheel, and not a cassette (it is one unit that threads onto the hub, right?) that is not designed/ramped/spaced for indexed use. Most likely you will need to replace the freewheel to make the indexing work. And yes, the slight wobble in the freewheel is normal.
If you stop to think about it for a minute, you'll see that the shift cable moves the derailleur which moves the chain. So the shifter has to pull exactly the right amount of cable to pull the derailleur exactly the right distance to make the shift. For this to work the shifter, derailleur and gear cluster all have to match.
I'm kind of thinking that your's don't.
Don't go to Halfords, support your LBS. They're far more helpful and are much more willing to give you a nudge in the right direction. I only went into Halford's once to see what it was like and was so disappointed with everything about it, just turned round and left!
Sounds like your components don't match each other as Retro points out. I once had a non-genuine shimano cassette which produced a similar effect on my MTB. Changed it to genuine, problem solved.
When I was a teenager 50 yrs ago, Fred Baker on Cheltenham Rd was the best bike shop in Bristol.