Sounds like the syncro rings
I agree with most of what's been said above although it's difficult to diagnose without being there. The F1 behavior you're describing does not sound like a clutch problem but does not sound normal regardless. Sounds more like syncro function to me -- especially in view of the fact that 2nd (and 3rd to a lesser extent) always see the heaviest usage. I hope a factory trained tech with factory SD2 or SD3 computer will be checking your F1. If not, you're asking for trouble.
There's almost no adjustment available for F1 function with the original '99--'01 TCU. The '02 and later TCUs provide much improved function and flexibility so you should at least consider upgrading. Changing gearbox oil is also a really good idea, especially if you're not sure when it was last changed. That would explain syncro function problems too. Then change it once a year or every other engine oil change, whichever comes first.
My '02 F1 coupe has functioned flawlessly with zero issues in over 4 years, but it sees regular usage and service at an authorized dealer. Congratulations! The 360 F1 is a fantastic car. Lucky you my friend!!
"Fear of guns is a sure sign of retarded sexual and emotional maturity." -- Sigmund Freud, General Introduction to Psychoanalysis, 1906.