In January 2013, a Twitter account posting news headlines which start with which two words garnered over 60,000 followers in a month? In 2019, it also launched a game in which people Google the two words followed by a random date and post the resulting headlines.

The Twitter account you're referring to is likely "Two Headlines" (@TwoHeadlines). In January 2013, this account gained popularity by posting fictional news headlines that start with the same two words, creating humorous and often absurd combinations. The account's unique concept attracted a large following in a short period.

In 2019, the account expanded its concept by launching a game in which people would Google the same two words along with a random date and share the resulting news headlines that appeared in search results. This added an interactive and participatory element to the account's content.

https://twitter.com/twoheadlines

The particular two words which fitted the requirements I was looking for was "Florida Man".