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I have been pulling apart hard drives for a while and have several cans of read/write heads laying around. Is there a category for just the read/write head or does it fall into something else?

If you’re talking about the entire arm vs the tiny head they go as dirty aluminium.
If your patient you can remove the ring coils as they’re usually copper, or aluminium/tin, or brass.
If you’re extremely patient and have many cans you may have enough to sensibly go after the tiny rhodium piece in the actual read head.

Boardsort doesn’t buy rhodium but some jewellery stores do.

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Yes, I am talking about the entire arm. So I guess there's not enough gold in the ribbon that connects to the drive to make it worth the time.

Correct. The metal ribbon with the contact wire connecting the pickup is usually tin nickel.
The laminate wire is gold but boardsort doesn’t buy it. There’s so little gold in them they cost more to process than value.
I mentioned in the flat wire sticky the best you can do is, if you have enough find a larger coin or jewellery shop and see if they’re interested.
If not just sell it as wire.

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After looking around I found a great detailed article on scrapping hard drives that answers my question here.

viewtopic.php?f=5&t=3978

Yep! We kind of go off track a bit after the second page though.

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