Your answer is just as fuzzy as someone selling the licenses would want it to be

An interesting fresh piece of information to consider is Oracle’s point of view: According to Oracle, the GPL license of MySQL Server does not “in most cases” in any way affect the license of your code that uses the server, such as a proprietary PHP script. This became clear during Oracle’s discussions with the EU and is documented in the EU decision (which is public, but a few hundreds pages long).

While this discussion has a long history in MySQL Ab, I must give it to Oracle that their take at least was very straightforward and easy to understand.

As I understand it, if you were to develop or find a MySQL client under a LGPL or BSD license, this would protect you from any legal bindings.
My interpretation of “linking” as as in C linker. Since the client only communicates to the MySQL server via TCP/IP (or UNIX socket), I do not see that it is linked with the server.
However, AFAIK, all major clients are GPL (or same as Perl license).

It’s an interesting issue, since the client is a relatively small and simple piece of code (compared to the server).