You will need to know all of the exact numbers.
A TD04-12T may have a thousand different revisions of the same basic model, and each one is slightly different-although they might look identical.
Turbo's are funny like that. They're spec'd by the engineers, may be revised a time or two before it makes it to production, and then the time comes to replace it, and guys just think that a T3 is a T3, when in fact that's a simplified easy to remember alphanumerical code that the entire aftermarket is familiar with, yet few realize that there are probably a couple thousand variations of a T3 (T3 used as an example). Sure a TB0344 466586-2X fits a Merkur XR4Ti and is strikingly similar to the ones found on turbo thunderbirds, but they ARE different (minor, but they are different). There's even different TB0344 4665xxxxx models, different turbine housings... That's only one example....toyota, Mitsu, Garrett/Airesearch, Borg-Warner, IHI, KKK, etc....there's millions of them...
A turbo shop (a good one, not a trucking outfit) can rebuild them cheaper than finding a new or even used one....or they can find you a core, ore whatever. I know a guy...his place has a funny name, but the man and his family are top notch with turbo's....try the G-Pop shop in Springdale, AR. Make sure to give him ALL the numbers off of your turbo. He might accidentally have one on hand, who knows, dunno if you don't ask him.