If an EMP event (NUKE BOMB) takes place your watch will be the last thing you need to worry about. Your skin falling off might be something you might want to deal with first.
My 1917 Elgin Pocket watch with the 23 jewel Father time movement will be ticking away EMP or not for a few more decades I venture
Not true on the first part. If an emp occurs you most likely won't even know it until someone tells you it did. 200+ miles straight up above Kansas isn't going to be heard in the NW.
Elgins are nice watches. I have my Great Uncles old Hamilton and a few more to back it up. Unfortunately, they need to be cleaned and reoiled periodically and that is getting more expensive as time goes on. The new synthetic lubes do last longer before hardening they say, so it will go many years longer before it needs service again.