What scriptures describe Shiva whispering Rama's name to those who die in Kashi?

Question

The Rama Bhujanga Stotra is a hymn to Rama composed by the Advaita philosopher Adi Shankaracharya. Here is what he says in verse 3 of the hymn:

yadāvarṇayatkarṇamūle'ntakāle
śivo rāma rāmeti rāmeti kāśyām ।
tadekaṃ paraṃ tārakabrahmarūpaṃ
bhaje'haṃ bhaje'haṃ bhaje'haṃ bhaje'ham ॥

I adore shrI rAma, the Unity, the greatest one, whose name is uttered in the ears of the blessed devotees in KAshi at the time of Death by none other than Lord Shiva Himself. This form/name of the Lord (tArakabrahma) is capable of rescuing devotees from the ocean of samsAra.

Now I'm familiar with the notion of Shiva whispering other things, like the Pranava mantra, into the ears of those who die in Kashi. And I'm familiar with the notion of Shiva chanting Rama's name in general. But my question is, what scriptures mention Shiva whispering Rama's name into the ears of those who die in Kashi?

By the way, the words "rāma rāmeti rāmeti" in the second line echo the famous "śri rāma rāmeti rāmeti" verse where Shiva tells Parvati about the glories of chanting Rama's name.

EDIT: I just found a reference to this notion in Tulsidas' Ramcharitamanas:

The might of Rama's name is immeasurable ; so tell the saints, the Puranas and the Vedic commentaries ; the immortal Sambhu, who is the lord Siva, the perfection of wisdom and goodness, is ever repeating it: though all the four groups of animate beings in the world attain to salvation if they die in his city Kasi, yet, O king of saints, it is by the virtue of Rama's name; and therefore Siva in his compassion enjoins its use.

ÉDIT 2: @Vishalprabhulawande points out that in this video, the Shankaracharya of Puri also says that Shiva whispers Rama's name into the ears of those who die in Kashi.

Answer 1

It is present in Padma Purana Uttara Khanda Chapter 243 Lord Shiva speaks Lord Rama as follows:

O Rama, we two are venerable to the world. You two (Sita and Rama) are always venerable to us. Gaurl mutters your name. I mutter your formula. To one desiring to die at Mani-karnika and remaining in half of its water I give your emancipating formula, giving (i.e. leading to) Brahman. [35-40]

Answer 2

रामनाम्ना शिव काश्यां भुत्वा पूत शिव स्वयम्। स निस्तारयते जीवराशीन् काशीश्वर सदा।।

Shiv samhita 2.18

Shiv himself gives Tarak mantra “ram” to those jivas who didn’t get moksh in Kashi.

अहं भवन् नामगृणन्कुतार्थो वसामि काश्यामनिशं भवान्या। मुमूर्षमाणस्य विमुक्तोऽहं दिशामि मंत्रो तव रामनाम ।।

Adhyatm ramayan 6.15.62

Shiv says: I always chant ram naam while residing in Kashi. There I use to give Tarak mantra ram ram to dying person…

उपदिशाम्यहं काश्यां तेऽन्तकाले नृणां श्रुतौ। रामेति तारकं मंत्र तमेव विद्धि पार्वती।।

Anand Ramayan yatra khand 2.15-16

Shiv says that he always ram naam while residing in Kashi and starts giving advice of taraak mantra “ram” in Kashi.

तत्रोत् क्रमणकाले तु साक्षाद् विश्वेश्वरः स्वयम्। व्याचष्टे तारकं ब्रह्म येनासौ तन्मयो भवेत्।।

Skandpuran 4.1.25.73

When the soul comes out of the body, then mahadev himself gives Tarak Brahm “ram” to the dying person.

यत्र साक्षान् महादेवो देहांते स्वयम् ईश्वरः। व्याचष्टे तारकं ब्रह्म तत्र एव ह्यविमुक्तये।।

Padmapuran 3.33.47

Mahadev who is himself ishwar gives Tarak mantra “ram” at the time of death while residing in Kashi

यत्र साक्षान् महादेवो देहांते स्वयम् ईश्वरः। व्याचष्टे तारकं ब्रह्म तत्र एव ह्यविमुक्तये।।

Kurma puran 1.31.61

Mahadev who is himself ishwar gives Tarak mantra “ram” at the time of death while residing in Kashi