> But when I set the value to `no' or `no-ding', I was expecting the
> point to automatically move to the third line immediately after typing
> "t" as mentioned in the above use case.

It was never intended to wrap around on typing a letter or yanking a text.
If such a behavior is a good idea, it could be added as a new value
to this variable.

Please try the following patch after setting isearch-wrap-pause to the
new value 'auto-repeat':