Tested out two fixes:

1. Can remove the assetPaths.json file from the .gitignore
2. Add a line to the .eleventy.js config to not rely on gitignore for the watch list (i.e. config.setUseGitIgnore(false)).

The drawback to the first solution is that any change will cause the assetPaths.json file to be updated, and marked as changed by git. It doesn't seem to make sense to commit this file, as it just stores a temporary hash.

The draw back to the second solution is that we would need to maintain a separate .eleventyignore file if there is anything else that we would like 11ty to ignore.

In addition to the above, I also tried a couple of things that did not work. I tried adding lines in the config to remove assetPaths.json from the 11ty ignore list in .eleventy.js, and to expliclity watch for it:

config.ignores.delete('_data/assetPaths.json');
config.addWatchTarget('./_data');

I've reached out to the cloud.gov pages team to see if there is another suggestion besides the two solutions above.

After reaching to the cloud.gov pages team @caleywoods, who worked on the template suggested removing the file from the local gitignore and instead adding it to the global gitignore. This worked great! But if someone doesn't have a global gitignore they would need to create a new file. Another alternative that seems to work is adding the file to the project local .git/info/exclude list

Marked as "later" due to not being a critical issue.