Connectors for computer cabinet fans

I have a few tower systems where one can mount fans on the side panels. This leaves the leads hanging, and they could easily be damaged when the panels are removed.

I've been looking for some kind of connector that I could mount on the panels and on the cabinet itself, one that would provide a connection when the panel is put in place. Perhaps with spring loaded connectors, or leaf connectors for sliding panels.

I'm sure such things must exist, but the problem is I don't know the correct search terms. Any engineers out there?