The solution is to allow TntConnect to "control your computer" in the Security & Privacy settings.

Checked the box to allow TntConnect to "control your computer":

Also, in the "Automation" section, TntConnect should be able to control "System Events".

Now TntConnect should be able to "Search for a Database..."

If you still can't use the "Search for a Database..." feature on your Mac

1. Open Finder. 

2. Under the "File" menu, click on "Find" (or click Cmd+F). 

3. Type in mpddb.