I believe there are a # of factors that contribute to 1 spouse wanting to come back.
1. changing youself. They grew tired of what you were, and they are scared that they will go back to the same routine. You have to change yoursef, physically, mentally, and emotionally.
2. They have to see what it will be like without you in their life. You have to be willing to let them see it. This is where the 180 comes in, and has to be followed. Once you start it, you must commit, and not be willing to care about anything they have going on in their lives (its hard with kids, but you get the jist) 1 of the best things I ever did, was take my son away for 3 days 2 weekends in row, and she was left with NOTHING TO DO, BUT THINK! 1 weekend we went racing outta town, and the next weekend we went hunting outta town. I made sure that that weekend was all about me and my kid. We had an absolute blast! It was his first time being with all the guys, and to this day hasn't stopped talking about it. My wife was going nuts, she told me it was the loneliest she has ever been in her life! That was the spark that started the fire, and got her thinking what it was going to be like.
3. SPACE! Nagging, pleading, begging, pushyness is a big fat unattractive quality, that noone likes!
as for knowing when they changed. I can tell you in my case it wasn't 1 thing. It was a # of different things, over a period of time. And quite frankly I needed it to continue before I was ready to reconcile. My W, started texting me about dumb things, started calling me about dumb things. Wrote me a letter telling me how sorry she was, and how stupid she was. She started making sure I knew where she was at all times. She started including me in her plans (this part really threw me for a loop). She wanted to be with me and our son, when we went to games, shopping, what ever. All these little things, let me know she was reengaged. don't settle for 1 little hint. Make her commit, just like she did you, follow the 180.