How Does One Resume Indexing After Pausing Indexing and Rebooting the Computer?

Rebooting your computer is fatal for the indexing process.  It will have to start the previous indexing process over again (which should be just for that last received resource).

It should restart automatically after reboot.   If it didn't restart on reboot, it should restart when you start Logos.  If not then you may have to force a full rebuild with "rebuild index".  But before you do that, you can check to see if a recent resource is indexed by searching for a phrase in that resource (i.e., select some text in that resource, right-click, and select Search Library). 

Another way to reindex a resource is to hide it (that is: add it to the hidden resources in the Program Settings), restart Logos, wait for the indexer to finish, unhide it, restart again, and the file  will be downloaded and indexed.  (You may have to run "Update resources" for it to detect that).

Pausing is available to relieve your computer of the CPU burden temporarily.  It does not allow the indexer to be stopped without loss of it's current work.