I haven't used vbulletin myself, but I think it stores the last login/post time of all members. When you display threads, check this time, subtract it from current time, and if it's less than what you want, put the signature between <!-- --> html code.
Although I really think that won't be fair to "old" members who have contributed to the forum with useful help/ posts.
You can instead do a check of "reputation" points/ number of posts etc before a signature can go live.
Thanks
