Hm... I just tried to do what you are aiming for and I have no problem with recording the steps and get the described result.
This is the flavor with the custom field for name entry and the script button:
If I enter the name of an existing vendor, the search help brings me the matching record:
If I enter a wrong name, I get the appropriate message:
This is the recorded (and adjusted) script:
This is actually rather simple... or did I misunderstand your scenario?
I had also no problem with selecting the search criterion 'Name' and was able to get to its properties... there is nothing special about this field, it's just a simple text box. Had to keep clicking on the field a few times since it's part of a tab and also a group box, but after a few clicks it was selected just fine:
I have no idea where the string TEST* comes from in your case (or how that recording was made for that matter, since it looks so different to mine).