Was blowing air to N64 Game Pack ever recommended?

No, it is not recommended.

The actual solution is the taking out and re-seating of the connection. Blowing air is something of a weird behavior. You risk blowing moisture onto the contacts and corroding them.

This type of connection is very common. In PCs, most of the expansion cards are using the same type of connection. However, you'll almost never find a competent PC technician blowing into the contacts.

The act of removing and re-seating these connection will remove some oxidization of the contacts, push aside dust, and generally can fix a simple connection problem. In my own experience fixing PCs, re-seating RAM is a rather mundane task that can fix weird errors on a PC.

Seems that Nelson's answer is right.

To further back up the fact that this was not actually a good idea, seems that Nintendo even warns about it. Found this label at the back of the Gamepack (how come I haven't noticed it before?):