There is a way - a bit Mickey Mouse though because I don't
have want to share my web server (opsec).

without the background

I just used a best-guess date for the halvening and a free countdown timer. You can sign up
here and you'll get 10,000 image opens on the free plan.
The timer is fairly customizable - I added the background image but you don't have to... I'm not sure exactly how large an image you could put in your sig though... maybe use it without the image and resize the fonts?
edit:
Also, you can get JSON formatted data with all the pertinent block info for free here:
https://api.blockchair.com/tools/halvening and enter that as a source at niftyimages which will enable you to grab info such as "blocks_left"
I set that one to update the JSON info every
15 5 minutes.
last edit: JSON updating every 5 minutes
If that were the case, it would be great to celebrate the next halving at NASA's research center. I don't know if it is possible to celebrate.