We’d need to actually see you playing it to be conclusive in advice.
Sanity check I’d try first: what happens if you just stay on one string? Can you maintain sync? If not, I wouldn’t even bother with a pattern that switches strings. Do a variety of patterns that stay on one string and focus on sync. Ones I have found most helpful are repeated 3 note groupings played as 16ths. There’s something special about it because it doesn’t let us get away with prioritizing patterns that must begin with the index.
Try it “reversing” that cycle too since you’ll need to play patterns in each direction.
There is of course the Yngwie 6 note pattern too, as well as Thunderstruck. The main theme to Yngwie’s Trilogy Suite (just stays on the g string) is another great hand sync practice piece.
All that said, if your hand sync on one string is solid, most likely there is a string switching issue. If so I’d try offsetting your pattern so it conforms to Gilbert 6’s
These are all just guesses and could be a waste of your time. Video will show what the real issue is.