It appears from the pesukim that she continued to wear "widows' garb" as a sign that she was waiting for the yibum to be done. This is different from the period of mourning or a woman not subject to yibum who would not wear mourning as a sign that she was ready to remarry. I do not have a source for this as it is from logic only.
וַיֹּאמֶר יְהוּדָה לְתָמָר כַּלָּתוֹ שְׁבִי אַלְמָנָה בֵית אָבִיךְ עַד
יִגְדַּל שֵׁלָה בְנִי כִּי אָמַר פֶּן יָמוּת גַּם הוּא כְּאֶחָיו
וַתֵּלֶךְ תָּמָר וַתֵּשֶׁב בֵּית אָבִיהָ:
Then Judah said to his daughter in law Tamar, "Remain as a widow in
your father's house until my son Shelah grows up," for he said, "Lest
he too die, like his brothers." So Tamar went, and she remained in her
This means that she lived as a widow while waiting for שֵׁלָה to grow up and perform Yibum (or Chalitza) with her. She would be unable to marry anyone else until he was ready.
וַתָּסַר בִּגְדֵי אַלְמְנוּתָהּ מֵעָלֶיהָ וַתְּכַס בַּצָּעִיף
וַתִּתְעַלָּף וַתֵּשֶׁב בְּפֶתַח עֵינַיִם אֲשֶׁר עַל דֶּרֶךְ
תִּמְנָתָה כִּי רָאֲתָה כִּי גָדַל שֵׁלָה וְהִוא לֹא נִתְּנָה לוֹ
So she took off her widow's garb, covered [her head] with a veil and
covered her face, and she sat down at the crossroads that were on the
way to Timnah, for she saw that Shelah had grown up, but as for her
she was not given to him for a wife.
This implies that she dressed as a widow (and not a single woman) in order to show that she was not eligible for marriage.
וַתָּקָם וַתֵּלֶךְ וַתָּסַר צְעִיפָהּ מֵעָלֶיהָ וַתִּלְבַּשׁ בִּגְדֵי
Then she arose and went away, and she took off her veil, and she
donned her widow's garb.
This again implies that as a widow who was not eligible to remarry, she dressed in a certain way that was understandable by the society in which she lived.