T509 1997 Speed Triple 2nd Gear Issue

Hi everyone,
i really need some help here.
I recently bought a wonderful T509 from 1997. Bike is perfect but after i've been riding it for a while (100 miles) i started having an issue (the last owner said he never had it, i doubt but i cannot demonstrate).

Bike rides very well, but when downshifting from 3rd to 2nd, 95% of the time it skips 2nd gear and goes straight to "N", so then i have to shift up to go in 2nd gear. I had a full engine oil change before even riding it.

You can imagine how annoying and unsafe it is.

Anyway, i just want to solve it but there is no specialized mechanic over here that has enough experience on these old Triumphs, and before putting someone else hands on my loved bikes i'd like to better understand what the problem could be with the help of some experts here.

Thanks guys!

 

thanks a lot for your suggestion, i'm going to investigate it and give it a try.