Won't go into 3rd gear upwards

[FinalImpact]

Inside the case is the shift drum. Either by hand or using a large pair of needle nose pliars, try to rotate the drum and feel all 7 locations.

Neutral
1st
2nd - 6th
Again - you will need to hand rotate rear tire a slight amount for it to 'drop in' to each detent fully.
Other than being ugly - the Flavorless shake is not really stopping the trans from shifting. **WELL MOST LIKELY** Unless the rust and degrading of the oil system has actually allowed a gear (slider) to seize to a shaft??

Point: if you can't select all gears by hand, by rotating the drum back and forth, there may in fact be issues inside the box with the lockouts and gears. Are both of those springs 100% OK? Do both of them allow the levers to center themselves? Are either broken?

WHEN is the last time it worked properly? Weeks, months, unknown?

Yes - clean it and OIL it with NEW fresh oil. Set the cover back on and attach at least the splined lever and test it. You don't need a new gasket to test it.

 

[TownsendsFJR1300]

What ever oil drain orifices you have in that cavity, if you can, use a wet vac with a hose shimmed down (to a, 1/4" ID maybe? to suck into the small orifices) to suck ANY/ALL debris out of there.

Once you get out what you can, I'd put it on the side stand and spray brake CLEANER all inside there. You want to loosen (and drain away) any and all small metal particles (so it runs off and away from the bike-use paper towels to catch/protect the bike).

Depending on how how much crap you find, I'd be doing at least one extra oil change to flush any metal that's in the oiling system.

 

[AlexdeCatt]

https://youtu.be/8MF6KWP-chA

inside was very stiff. At the time I didn't know if it was meant to except when someone said something about it. Thank you. Cleaned it withave washing up liquid and got it moving. Re oiled it and changed the oil. Now it works like a dream. thanks guys.