Hi,
there is no way to restrict the scope of the form's search box. So you definitely would have to create your own text box.
I would not consider it very intuitive for the general search box to only search the control/field where the cursor had been before he had to set it into the search box itself. It is in a different section of the form with no visual connection to a particular
control.
In addition many users already are aware of Ctrl+F from almost any application/environment. They don't have to leave the current control and in Access the default setting in the search (dialog) is to be limited to the current control...