Transmission pulled for 2nd gear death jump ...on undercut transmission?


just dropped my transmission and checked the gears, the figuring its a 13 year old bike it obviously needs a looking at and maybe an undercut tranny

checked the gears and they are all undercut, looks quite well too, cant actually see any damage on 2nd or 6th driven, every gear looks ok apart from 3rd and 4th drive but i have no issues with those gears only 2nd gear?

also to note, the selector fork that moves 6th into 2nd driven has obvious signs of wear, could that be my only issue? or am i missing something here?

thanks for the help guys!
by no means an expert but I think the shift forks have a min thickness value...could be bent...slop on the shift shafts...could be bent...while you are in there replace on the heavy side....if it is a stock engine it might be a waste of money to over build it. what did it feel like before you took it apart / did it get worse as time went by?
I have a new 6th gear and fork but im worried ill do all this work and still have the same problem
Literally the only issue is I boot it in second and it slips with a single clunk

Shifting into all gears is fine even moderate power in 2nd is ok its just a heavy acceleration causes a clunk and sudden judder

thank you for your reply sorry for the spelling mistakes damn touch phone and oily hands!
Trust me if it is jumping out of gear, it needs to be recut!

Here is where i have been send the last few i have had done this year, they work fast and awesome quality of work.
M/T PERFORMANCE - Tranmission Undercutting

They will do just the second and sixth, or have them do the whole rack.
Well this is the thing the new 6th gear I got is undercut but not on the 6th to 2nd teeth side
The old 6th and 2nd isnt undercut either?