Well, it has taken a while to figure out and fix but here is the solution:
The SQL databases in question needed to have 'Guest Account Enabled'
1. QlikSense was installed onto its own server with the engine services attributed to LOCAL SYSTEM
2. LOCAL SYSTEM within SQL Server 2012 is [something like] the login NT AUTHORITY\SYSTEM under server>security>logins
3. Within the Properties for NT\AUTHORITY\SYSTEM under Server Roles, enable roles for dbcreator, diskadmin, processadmin, public, serveradmin & sysadmin
4. Flip to User Mapping (still in Properties) and check each database required, is ticked 'Guest Account Enabled'.
As a precaution, stop and restarted the QlikSense Engines.
Hope this helps....reach out if anymore information needed.
*Thanks to Differentia Consulting for initially pointing in the correct direction*