Alex Wheeler
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If all is well and correct with the firing pin/cocking piece/bolt, I would think that the problem lies within the trigger that you say is "2nd hand".
I have experienced before a jewell trigger that was used and had been sitting in a safe for 5 years. The trigger would not reset and the firing pin would follow the bolt back down as it was rotated closed.
After a good cleaning with brake cleaner and lighter fluid to remove the old gummy residue inside the trigger, all was well.
I understand that yours will reset if you pull the bolt back a small amount, making me think that your 2nd hand trigger could be just a slight bit sticky inside....or not. Goodluck!!!
It is normal to have to pull the bolt back a little to allow the trigger to reset on and action that has cock on close.