Can anyone recommend a free email countdown? -without branding-

I doubt there are easily findable service that offers such without branding. You can though find some code snippets from github for example: https://github.com/search?q=emai... Those you could host on your own website, and have it as you like. Or you could get something like that deployed as AWS Lambda or similar serverless solution. All those though need some knowledge to get it done, so not sure if that constitutes being "free", if you don't have such knowledge yourself, or within your team.

Pretty sure most are going to use branding. They need to monetize somehow. Could always build your own - probably very simple.

If it's free, there is a 99% chance they will brand it. For the amount of time it takes to find what you are looking for, it may be more worthwhile to save time and pay the lowest fee instead. All the best!