It seems from this document 
<https://cloud.google.com/tasks/docs/reference-access-control> that what 
you have granted permissions for Cloud Tasks for should be sufficient as 
cloudtasks.queues.update is needed to modify an existing task. 

It does seem that that appengineDeployQueue is App Engine-specific Gradle 
task  
<https://cloud.google.com/appengine/docs/standard/java/tools/gradle-reference>which
 
likely means it requires App Engine roles 
<https://cloud.google.com/appengine/docs/standard/java/access-control> and 
perhaps additional actions to use Gradle plugin 
<https://cloud.google.com/appengine/docs/standard/java/tools/gradle> if you 
have not done so yet. 

This will likely require investigation into your permissions so I suggest 
opening an issue tracker 
<https://issuetracker.google.com/issues/new?component=187191&template=0> if 
the above suggestions do not resolve the issue. Please note I provided all 
documents in App Engine Standard format but Flex documents should exist. 

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