Had a similar problem in a ae82 i had with a 4efte, not the same at all i know. But mine wouldn't turn off because the ignition switch was stuffed. happened all of a sudden after a long drive (250km, long for me as it gets me to the other end of the state). I also had to stall it to get it to stop. worth looking at maybe
only suggesting this as it reads to me that by "running on" you mean it'll keep going till you do something about it