It’s not so much neurological as psychological.
Whatever it is, it is not logical.
Logic gets you nowhere, with stuttering.
The cure is as simple as stepping backwards, outside your skull, and not-caring.
As for vitamins and supplements: well, good nutrition can only help, in a general sort of way. But the stutter is a frozen-up set of gears, solidified by stress.
Un-stress. Ease up. Let go. Walk away.
Leave that stutter in the past, and move ahead into the future.