Do I need to add a new single column index to a table if a multi-column index on that field already exists?
No, not at all !!! The MySQL Query Optimizer will do the right thing if the main column(s) needed is leftmost in the index. If you did make such an index, the MySQL Query Optimizer may opt never to use that index if you always perform GROUP BY job_id,keyword_id. MySQL Query Optimizer may or may not use the index if you gather records by job_id only, but then you have a redundant index wasting space anyway.

If the table is MyISAM, making such an index would just bloat the MYI file.

If the table is InnoDB and innodb_file_per_table is 0, making such an index would just bloat ibdata1.

If the table is InnoDB and innodb_file_per_table is 1, making such an index would just bloat the .ibd file of the table.

In summary, you do not need to make that additional index !!!