This tutorial will guide you into configuring a custom level permission and updating the permission of the crawl user. Be aware that this has to be done for every site collection that needs to be crawled.
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Step 1: Create the custom permission level
Go to the desired site collection and log on with a site collection administrator (or any user authorized to edit site permissions).
Click
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Site Actions
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> Site Permissions
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(your user should see this
...
option with sufficient privileges).
Click
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Permission
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Levels (It could take some time for it to enable, so wait until it does).