When you say "test DB connections in Eclipse", that can mean one of 2 things.
Eclipse has an optional database plugin that allows you to use Eclipse to make connections (via JDBC) to SQL database servers and run SQL and DDL commands and queries.
However, since Eclipse is also an application development environment (
IDE), it is used to create JDBC applications. Since Java applications can run stand-alone, they don't depend on Eclipse for help and in this case you'd be using the Java debugger to run the app using a debugging (Run) profile.
The essential difference in terms of JDBC is that for the Eclipse database plugin, you have to tell the plugin where to find the JDBC driver jar(s) that you want it to use, then use the plugin GUI to define JDBC connections that you'd issue your SQL commands through.
In contrast, when testing/running a stand-alone JDBC application you would have to include the JDBC driver jar's location as part of the classpath you set up under the Run/debug menu dialog.
Depending on what database you are using, what OS you are using, and how you install things, the location of the database JDBC driver JAR could be located anywhere. For me, I'm using the Fedora Linux OS, and its standard software package installer for MySQL JDBC puts the jar in the /usr/share/java directory these days. The location of the driver really doesn't matter, though, as long as you point the application you are using at it.
If you get error messages, however, please tell us what the text of those messages is. We can help you much better that way.