Chrono seconds hand 3590.50?

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Am I correct in thinking that this chrono hand is incorrect for the 3590.50 reference?

 
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That chrono hand style appears on the new FOIS and on certain models of 2915 / 2998 but never on a Professional
 
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Okay, as I thought, it should have a flat bottom and a spade shaped (what's it called?) tritium filled piece like the photo.

Any ideas where I could I source one - tritium or superluminova? Are they interchangeable between professional models?

 
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Found this on the bay but wants £50 for it. Looks to me like it's missing a pivot sleeve to secure the hand to the post. Unless it's pictured the wrong side. Sorry about my naming of parts incorrectly I am sure.

Edited:
 
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Curious. Offrei offers three sweep second hands for the cal 861 - each a different length, 14mm, 14.25mm and 14.75. My thinking is that the 14.75 is correct for the 3590/3570 ref and the other two for the reduced? Can someone set me right on this.