Corvette Shifting Problem

My car is a 2003 Corvette with manual 6 speed trans. Occasionally when attempting to shift from 4th to 5th at normal speeds it wants to drift too far over to the right in the neutral pattern. If I were to push it up, it would grind the reverse gear. Is there a weak spring or something causing this? I can’t find any info (TSBs or chat info) about this. Thanks for your advice. Your show is THE BEST!

While the pattern is spring loaded to bias it toward upshifting as you move through the gates, you should have a reverse lockout.

I’m not detailed familiar with your linkage, but I’d get a repair manual and look at the reverse lockout details.

It could be a malfunction with the 1st-to-4th interlock.