Take some proto-board with plated-through holes, cut to size to match the side of the cassette. Drill/file out some registration notches to match the plastic protrusions next to the pogo pins. Determine which plated-through holes match up to the pins and attach wires to the protoboard for each signal. Cover with some electrical tape and clip it on with spring clips of some sort. And of course bundle your wires into a harness and connect them to your amplifier/antenna. Plenty of ways to improve on that, but quick and dirty should work.
That lock switch looks interesting. If you figure out how that works, you might be able to rig something to engage that instead of using a clip.