[Tmontague]

To add an anecdote to what others have stated:

My 2010 3.6R had an external headgasket leak on the top of the drivers side . It leads to pooling of oil on the top of the engine and it eventually goes down the front timing cover. It looks terrible but I have driven it this way for 45k km and it has never posed an issue. I do use a high mileage 5w30 in it which helps with oil leaks. Just recently has the leak gotten bad enough to where I am going to fix it at the end of the summer. It doesn't use a lot of oil bit it is too messy for me and it's starting to bug me.

 

[Tmontague]

EZ36 is a completely different design, and very rarely leak oil from the head gaskets. Far more likely to be chain cover or something else. If it is the head gasket, that means it's a high pressure passage, which likely means you have a pressure drop to your valve train on that side....

The EJs leak oil because oil sits in the return passages between the head and block while the engine is off, and they used a coated single-layer gasket which does not hold up to sustained oil exposure. EZs use an MLS gasket

I am aware of the obvious design differences of the ez36 and an ej - I was offering an anecdote to the OP's original question, that yes HG can fail and only have an external oil leak.

And unfortunately my engine does have an external HG leak, as well as a timing cover leak, upper oil pan leak. Hence the reason I am going to the trouble of pulling the engine to re seal it.

Although not overly common, ez36d's can/do experience HG leaks at high mileage and they most often are of the external leak type. Rarely do they fail internally and lead to cooling issues. This is why so many people are able to ignore them and keep on truckin'.