Would it be feasible to build an arduino that takes 12v on/off signals from a vehicle diagnostic port (1984 pre-OBD)?
Yes, it is possible. The 12v signals would have to be conditioned for the Arduino to receive them (0 - 12v or maybe 0 - 12-14.5v?). Then the Bluetooth side would be the same as any other Bluetooth data transmission.

So your question comes down to: Is this a fun project that's worth the effort you put into it for the learning experience? Or is this meant to answer a need, and the most practical means to that end is the best means?

Ex: I wanted to know how long / what kind of driving would it take to get my car's oil to full temp (~100C), starting from dead-cold in the winter? I had a thermo-logger I'd built for another experiment, so I taped a sensor to my oil filter (yeah, not the greatest, but quick and dirty) and lead a cable outside the hood, through the driver's window, to the experimental PC board on my dash-board. It wasn't a miserable failure but nothing to be proud of, either.

The solution I settled on was a USD$12.00 OBD port sender and an iPhone app. The results were much better, and while I didn't have the built-it-myself experience, I got the data and the answers I needed.