We see this in the case of Elisha. Elijah asks him to "tarry here" three times, and Elisha always replies in the same way, "As the lord liveth, and as thy soul liveth, I will not leave thee."
Here is one example:
- ו וַיֹּאמֶר לוֹ אֵלִיָּהוּ שֵׁב-נָא פֹה, כִּי יְהוָה שְׁלָחַנִי הַיַּרְדֵּנָה, וַיֹּאמֶר, חַי-יְהוָה וְחֵי-נַפְשְׁךָ אִם-אֶעֶזְבֶךָּ; וַיֵּלְכוּ, שְׁנֵיהֶם.
6 And Elijah said unto him: 'Tarry here, I pray thee; for the LORD hath sent me to the Jordan.' And he said: 'As the LORD liveth, and as thy soul liveth, I will not leave thee.' And they two went on.
~Kings II 2: 6
Something similar occurs with Ruth and Naomi, where Naomi very eloquently attempts to tell Orpah and Ruth to remain at home, and while Orpah returns, Ruth states that:
- טז וַתֹּאמֶר רוּת אַל-תִּפְגְּעִי-בִי, לְעָזְבֵךְ לָשׁוּב מֵאַחֲרָיִךְ: כִּי אֶל-אֲשֶׁר תֵּלְכִי אֵלֵךְ, וּבַאֲשֶׁר תָּלִינִי אָלִין--עַמֵּךְ עַמִּי, וֵאלֹהַיִךְ אֱלֹהָי.
16 And Ruth said: 'Entreat me not to leave thee, and to return from following after thee; for whither thou goest, I will go; and where thou lodgest, I will lodge; thy people shall be my people, and thy God my God;
יז בַּאֲשֶׁר תָּמוּתִי אָמוּת, וְשָׁם אֶקָּבֵר; כֹּה יַעֲשֶׂה יְהוָה לִי, וְכֹה יוֹסִיף--כִּי הַמָּוֶת, יַפְרִיד בֵּינִי וּבֵינֵךְ.
17 where thou diest, will I die, and there will I be buried; the LORD do so to me, and more also, if aught but death part thee and me.'
~Ruth 1: 16-17
- ה וַיֹּאמֶר אַבְרָהָם אֶל-נְעָרָיו, שְׁבוּ-לָכֶם פֹּה עִם-הַחֲמוֹר, וַאֲנִי וְהַנַּעַר, נֵלְכָה עַד-כֹּה; וְנִשְׁתַּחֲוֶה, וְנָשׁוּבָה אֲלֵיכֶם.
5 And Abraham said unto his young men: 'Abide ye here with the ass, and I and the lad will go yonder; and we will worship, and come back to you.'
Similarly, when it comes to the situation of the pilegesh b'Givah, staying behind is what gets the man and his concubine into the subsequent debacle. Although, of course, he does not tarry there that particular evening, it is the fact that he tarried there the nights before that prevents him from leaving when he should have, and making it all the way home in time.
- ח וַיַּשְׁכֵּם בַּבֹּקֶר בַּיּוֹם הַחֲמִישִׁי, לָלֶכֶת, וַיֹּאמֶר אֲבִי הַנַּעֲרָה סְעָד-נָא לְבָבְךָ, וְהִתְמַהְמְהוּ עַד-נְטוֹת הַיּוֹם; וַיֹּאכְלוּ, שְׁנֵיהֶם.
8 And he arose early in the morning on the fifth day to depart; and the damsel's father said: 'Stay thy heart, I pray thee, and tarry ye until the day declineth'; and they did eat, both of them.
ט וַיָּקָם הָאִישׁ לָלֶכֶת, הוּא וּפִילַגְשׁוֹ וְנַעֲרוֹ; וַיֹּאמֶר לוֹ חֹתְנוֹ אֲבִי הַנַּעֲרָה הִנֵּה נָא רָפָה הַיּוֹם לַעֲרוֹב, לִינוּ-נָא הִנֵּה חֲנוֹת הַיּוֹם לִין פֹּה וְיִיטַב לְבָבֶךָ, וְהִשְׁכַּמְתֶּם מָחָר לְדַרְכְּכֶם, וְהָלַכְתָּ לְאֹהָלֶךָ.
9 And when the man rose up to depart, he, and his concubine, and his servant, his father-in-law, the damsel's father, said unto him: 'Behold, now the day draweth toward evening; tarry, I pray you, all night; behold, the day groweth to an end; lodge here, that thy heart may be merry; and to-morrow get you early on your way, that thou mayest go home.'
~Judges 19: 8-9
- נה וַיֹּאמֶר אָחִיהָ וְאִמָּהּ, תֵּשֵׁב הַנַּעֲרָ אִתָּנוּ יָמִים אוֹ עָשׂוֹר; אַחַר, תֵּלֵךְ.
55 And her brother and her mother said: 'Let the damsel abide with us a few days, at the least ten; after that she shall go.'
נו וַיֹּאמֶר אֲלֵהֶם אַל-תְּאַחֲרוּ אֹתִי, וַיהוָה הִצְלִיחַ דַּרְכִּי; שַׁלְּחוּנִי, וְאֵלְכָה לַאדֹנִי.
56 And he said unto them: 'Delay me not, seeing the LORD hath prospered my way; send me away that I may go to my master.'
~Genesis 24: 55-56
I'm sure this appears in the Motif Index somewhere, but I do not know the number of the classification.