It's the same engine in both.
If same engine and transmission models, yes.
The check engine light on a 2005 Jeep Grand Cherokee looks like this... Here is a link Check Engine Light It looks like a little yellow engine.
Check: Autotrader.com KBB.com Nada.com
With a scan tool.
There are pages and pages of things that can cause a check engine light. You need to have it checked with a scantool. Then the code can be diagnosed and repaired.
That is the check engine light.
The engine computer is the regulator.
The 2006 Jeep Grand-Cherokee has a V6 engine.
The 2013 Jeep Grand-Cherokee has a V6 engine.