I think any governors from the Republican Party who go on to win the presidency will have emerged from base states for the Republican Party for a general presidential election.
I think the same with governors from the Democratic Party who go on to win the presidency will have emerged from base states for the Democratic Party for a general presidential election.
Republican base states: Alabama, Alaska, Arizona, Georgia, Idaho, Indiana, Kansas, Kentucky, Louisiana, Mississippi, Missouri, Nebraska, North Dakota, Oklahoma, South Carolina, South Dakota, Tennessee, Texas, Utah, and Wyoming.
Democratic base states: California, Connecticut, Delaware, Hawaii, Illinois, Maine, Maryland, Massachusetts, Michigan, Minnesota, New Hampshire, New Jersey, New York, Oregon, Pennsylvania, Rhode Island, Vermont, Washington, and Wisconsin.
The Koch brothers would love to get Wisconsin. But, only if this country turns totally into the hellhole of their evil vision.
As for such states as Arkansas and West Virginia, they're still electing Democratic governors. (Montana as well.)
The battlegrounds/bellwethers, not mentioned, make me less confident. (Perhaps they're considered a better strategy for selection with a vice-presidential running mate.)
Also keep in mind this: Over the last 100 years (kind estimate), Bill Clinton (D-Arkansas) was the only president of the United States whose home state did not rank among the Top 20 in population.