I believe UAN is right. When you can give it to him without all of these doubts and questions, it is the right time. If you felt good about giving this special watch to him, you wouldn't have asked us about it, much less set up a poll.
The watch may not be significant in difficult child's mind, and in my opinion that alone means this is not the right time to pass on a family heirloom. No matter how much he does or doesn't treasure family, his history, or heirlooms, he just isn't likely to be ready to keep track of this. I think that he will be someday, and on that day you will know that it is time to give it to him.
It may be a gift for a young man taking his first adult steps, but the nature of those steps has changed hugely since our grandparents' times. difficult children need a few extra years to get to where past generations were when they left high school. I think the gving of any gift should be done with where/what the person is ready to handle in mind. Right now? Your son is dealing with an awful lot of pressure and scrutiny. while it may not be this way for us, for many of our kids a gift like this comes with expectations. While I might see the watch as a hug from my grandpa, my difficult child would likely see it as a sign of yet another person who expects him to act a certain way and another person who's expectations he cannot satisfy, so why even try?
I have NO idea why my difficult child thinks this way, and it took me a very long time to understand and accept it. When he was little we told him that coat or shirt or blanket from a grandparent was a hug every time he wore it or used it. We taught this to all my kids, largely because we lived several states away for quite a few years. So this was a way to foster their relationship in a way they understood. Wiz esp used to LOVE going to thrift stores with me to find 'hugs' for Gma and Gpa. But in later years he didn't want ANYTHING that reminded him of any family member. He said he could not make us happy with him, and he didn't care to try, and he didn't need the 'guilt trip' of family heirlooms that just showed that he was a failure. This is slowly changing, but it is still his thought process.
It might be that difficult child would only see an old watch, not the heirloom you see. He is also at an age where kids are notorious for walking away from possessions, and I think you would be upset if he lost, sold or pawned it, or it was stolen. Until you can give the gift without the strings of expectations and check-ins to see if he still has it? Then neither of you is ready for the watch to transfer from your possession to his.