Half terms and term limits

[President Johnson]

How do states with a gubernatorial term limits handle half terms? Are lieutenant governors, who become governor via ascension rather than election and serve to finish the ongoing term eligible run twice? Or is there the same rule as at the federal level: A succeeded vice president can run once if there is more than two years left in the term, or twice if there is less than two years (LBJ being eligible in 1964 and 1968, while Gerald Ford would have been term-limited in 1980 if he won 1976).

Some interesting situations:

- According to Wikipedia, South Carolina governor Henry McMaster has already filed to run in 2022. Even if South Carolina applies the same rule as at the federal level, McMaster would be eligible to run again because be became governor on January 24, 2017, shortly after Nikki Haley's second term went into its second half.

- In Missouri, Governor Parson is expected to be elected to a full term this November. Is he term-limited in 2024, since he served more than half of Greitens' term?

- Oregon obviously counts Kate Brown's 2015-2019 as first term (though she was reelected in a special election in 2016 and then reelected to full four years in 2018). She will termed out in 2022.

- I think we discussed Virginia some years ago. It has never been tested before, but a governor in Virginia could actually run as an incumbent if he succeeded to office the first time. I actually looked this up in the state constitution, but it didn't answer the question.

The only lieutenant governor I remember succeeding to the governorship and being elected more than once is Rick Perry, but Texas has no term limit.