One trait that many types and instances of ellipsis have in common is that the appearance of ellipsis is optional. The occurrence of VP-ellipsis, for instance, is often optional, e.g. He will help, and she will (help), too. Whether or not the second occurrence of the verb help is elided in this sentence is up to the speaker and to communicative aspects of the situational context in which the sentence is uttered. This optionality is a clear indication of ellipsis.
Although the article continues on to describe exceptions, the above makes for a good rule of thumb: a sentence that is considered to contain ellipsis (of the standard sort) must communicate identically whether with or without the ellipsis.
As such, the grammar of both forms follows that of the full (no ellipsis) form.
If you consider "He might've turned his head and seen the incident" to contain ellipsis, it would be natural to consider the full form to be:
- He might've turned his head and he might've seen the incident.
Grammatically, you can't substitute saw for seen in that sentence, so saw doesn't work in the ellipsed version, either.
Now, you could argue that the conjunction has two elements:
- He might've turned his head.
- He saw the incident.
In this case, you'd argue that only the word "he" was elided: "He might've turned his head and he saw the incident".
However, this feels unnatural. I suspect it has something to do with the uncertainty of "might have turned" contradicting the certainty of "he saw", where the seeing appears to be contingent on the turning. Alternatively, we might consider the modal verb might to be so dominant that it naturally attaches to both parts of the conjunction, so saw doesn't work because * might saw doesn't work, grammatically.
Either way, if we provide the second part with an explicit modal, the sentence works again:
- He might've turned his head and he definitely saw the incident.