You can't fill it, unfortunately. You just have to look it up or ask people. I guess it was a system designed to encourage people to cooperate and share information, but these days there's third party tracker sites for everything and no one's going to bother remembering the time and slots for the dozens of different rare materials in the game, so it's just kinda annoying. I wish the gathering log would update with the time and slot once you have successfully gathered that item.