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Did you install a drive temp monitoring program? eg. MacsFanControl or iStat Menu? If so, that may be the cause.

The light should not blink constantly otherwise, only when it is being actively accessed.
I’m sorry I think you’re confused.
 
I’m sorry I think you’re confused.
If I am confused, then it is because your post is confusing. You said it is constantly blinking when the drive is live. It should not do that. It should only do that when actively accessed, as I already said.
 
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