This thread inspired me to throw some Maiden on my turntable and try to cop some basslines...only partially successful, but a lot of fun.
I found for me to really nail that tone comes from what others have said - it's all about the right hand attack. Usually when I play I'm using the bottom of my fingertips and sort of pulling them across the string (the blue X's in the pic).
To get that Harris "clank" I use the very top of my fingertips and quickly and powerfully come down (the red X's in the pic).
Sure the type of string and your bass and amp's EQ's will play a part in getting that tone, but it's mainly perfecting that right hand technique.