It may be that an old cassette tape head will be able to get an output from the stripe. If you can get the format of the data, you can probably kludge up a reader.
Why build one? Just rip one off the face of an ATM/ABM that some crook put on there to piggy back on the legit one. They're making exact copies of the front of the ATM machines and fitting their own readers to them. When placed on the machine they are almost undetectable.
You can buy ones for cheap. I guess you could just open em up and see whats inside. I'm sure you can build one its just are you willing to order parts? or just want to salvage parts?