In my 15+ years of web development, there are very few things I can say are unequivocally a good idea. It almost always does depend.
Storing timestamps instead of booleans, however, is one of those things I can go out on a limb and say it doesn’t really depend all that much. You might as well timestamp it. There are plenty of times in my career when I’ve stored a boolean and later wished I’d had a timestamp. There are zero times when I’ve stored a timestamp and regretted that decision.