Hi there,
 I’m having trouble shifting up through the gears when accelerating, shifts okay when riding gently. Any idea where the problem might be ?
Thanks,
Stefan

Hard to diagnose. Are you shutting off as is usual for the second it takes to change gear.
Are you using the clutch while changing gear.
I have to admit--hang my head in shame--i don't use the clutch & just snick it through on my 360, never a problem.
Maybe i use it when necessary without thinking--subconsciously.
I know i use it to start off & for stopping haha.
I'd better double check that statement & think i use it on my 175.
I'm only divulging my secret in that--if mine changes easily then yours should do even better using the clutch.
I'll leave it there [& wait for the flack from everyone] haha.
So here's an idea. Sit on the bike & without motor running, change up & down through the gears.
You'll need to rock it back & forth an inch or two while doing this for the internals [dogs] to slot in but should click up & down effortlessly.
I'm now suspecting a problem with centralizing the gearchange which really shouldn't alter unless you've fallen hard on the gear lever or bike has landed on a tree stump in the forest
There's two eccentric screws in those older 360's. One to equalize the maximum travel each way--then after setting that one--then set the smaller one to centralize it to get equal free movement to pickup the next drum pin to go up--or down changing.
Just hook it up to say 3rd or 4th gear by hand [no motor] & then by hand on the lever feel how much springy free travel before you touch the next pin to change gear.
Should be equal up & down play on the lever [in a perfect world].
Can be slight variation but important thing is that it pics up the next pin.
If it goes way up--like full travel but getting nowhere, but will change down ok, then sounds like you issue is in those adjustments.
One other random unlikely thought is have you changed the oil & taken out the change plunger & spring [fell out in the oil tray], common mistake 'that'.
Drain bolt 17mm socket size is in the middle.
Plunger bolt is on the left at an angle underneath. Maybe 17mm also but could be 14mm.
Very sorry for the long story--are you still awake. If so, check the last idea first although gearchange would feel very vague & miss gears--jump out etc-- if plunger was missing.

Re-reading your post. Probably nothing i said above is relevant if its only when accelerating & ok cruising. Sorry about that--rethink time.

Any and all tips are relevant, I appreciate it. I have just clicked up and down through the gears effortlessly, engine off, bike stationary and no clutch. I’ve just realised that the clutch isn’t fully disengaging even after adjusting it as far up as possible at the handle bars. I was about to pull the right side engine cover and take a look. I’ve read somewhere the rubber O rings can be troublesome and can be removed without much concern.

Yes remove them. New fibers would be good too.
But does seen odd & if clutch was failing to free properly when changing at speed it'd be hanging on that bad that when stopped you'd have no chance of finding neutral & would try to keep pulling.
When the fibers are out just check the hub revolves free from the basket. Bit of a mystery--to me. See what others come up with.

Any and all tips are relevant, I appreciate it. I have just clicked up and down through the gears effortlessly, engine off, bike stationary and no clutch. I’ve just realised that the clutch isn’t fully disengaging even after adjusting it as far up as possible at the handle bars. I was about to pull the right side engine cover and take a look. I’ve read somewhere the rubber O rings can be troublesome and can be removed without much concern.

  

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