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The binding does in fact indicate the solenoid is failing. That being said, removing the fuse and having the issue vanish could in fact mean the issue is nothing more then dirty fluid and some varnish built up in the solenoid or the tube that goes to the transfer clutches.
What I would do is have a transmission flush done. With this service you do not have to replace the filter, it can clean the varnish from the valve body and the solenoids, and it will replace ALL of the atf in the transmission.
If the problem comes back after that service, then I would have the clutch pack and solenoid replaced to resolve the issue.
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