How exactly does a stock price gap overnight?

A stock price is the price where two entities are willing to transact. The prices are often affected by new information. If a company has a major announcement to make during the day, trading is often halted, and then the price can be radically different after trading resumes, since investors may have revised their valuations.

The way I always thought of it is that just before the market opens, the exchange matches and executes all "overlapping" orders that accumulated during the weekend. The first price posted after the bell is consequently the new equilibrium, which will differ from the closing equilibrium if supply and demand have shifted while the exchange was closed.

The only person that could properly answer this question though would probably be a software engineer working on the order matching engine that the exchange servers run.

When there is news, order flow shifts to one side, often creating an order imbalance. Where the stock opens depends on price matching and the opening price will be one that best clears the market.

The KODK news was the worst kept secret. Share price rose nicely for two days, before the announcement.

You stated:

If anyone has the stock chart that includes these hours, please edit this post.

I have access to Time & Sales. What information are you seeking?