If last build failed, thus the integration failed, for a non-persistent error (disk problem, licensing problem ...) rebuilding the job can succeed if no other build have been executed since last time.
If you have done a job configuration change, and need to trigger the job to test the configuration you typically need to make a commit that triggers the job. Push a commit to a ready branch, or wait for one.
There is a work around, that often enables you to build manually: Make the job parametrized with BRANCH_TO_BUILD and use that variable in the 'branch specifier'. Make BRANCH_TO_BUILD have the default ready-branch specifier, so if not given the job works as if there were no parameters. If you now build the job manually, you can type in a branch to build.
Failed and ‘Nothing to do’ statuses when merging
Failed builds can happen if there is a merge conflict which cannot be solved by a merge. In this scenario it is up to the user to merge the integration branch into their own development branch to fix their issues and deliver it again.
How Pretested Integration uses credentials
The Pretested Integration plugin will re-use the credentials for configured for the SCM that performed the merge. That means that if you've properly configured credentials in your git plugin, that is, credentials with write acces to your repository no further configuration is required.
The recommended setup and git workflow