Ungrouped Server Index

The indexing will continue to run on the server where the indexes are located.  Even if you create separate vault stores for archives and move the archives the indexes will remain in the current location.  The only way to "rebalance" the indexes is to physiclally copy the indexes to a new location then then use the "Manage Index" wizard to repoint SQL to the new location.  It is a very manual and intensive process. 

Alternatively, you can close the index locations on the old server, forcing EV to create any new indexes on the new server.  The old indexes will remain in use but no new indexes will be created.

Agree, move some or all of the Indexes. I assume you're using EV10/11 and can use Index Server Groups to (crudely) balance the Indexing load.

I did similar in EV9 albeit using a dedicated Indexing server, Indexing seemed to be the most intensive process in our environment, https://www-secure.symantec.com/connect/blogs/ev9-moving-indexes-new-server.