I don't know much how second marriage rituals take place, but I have heard from my family members
about the tradition where younger brother marries elder brother's wife, if he's single (or sometimes with consent of first wife due to some major circumstances) when she's widowed, because a woman was never supposed to remove her sindoor etc, once married.
Also in some customs it is allowed for a widow woman to continue putting sindoor if her demised husband had asked her to do so as his last wish.
Also I have seen my science teacher who used to put sindoor after her first catholic arranged marriage, but never put sindoor after her second marriage which is love marriage in Hindu style.
On the other hand, my computer teacher when I was in 4th std, who lost her husband just after 1/2months of marriage always wear faded clothes, no bangles, no rings, no earrings(except small tops that too occasionally) & only a small black bindi. Still she looks so beautiful with that simplicity.But when I saw her after her second marriage I was completely mesmerized, wearing a red saree, with 1&half dozen bangles, jhumka, designer bindi and her hair partings fully filled with sindoor. She's is looking more beautiful than before.
In our tradition also, one year is the waiting period after death of anybody in the family, before any auspicious work took place in the family.
But with changing time it has reduced to only till all death ceremony functions are completed.