We have quite a few narration which say that the believer seems the Imam's (as) on his death bed.

Hadith 1:

النضر بن سويد عن يحيى الحلبي عن عبد الحميد الطائي قال:سمعت أبا عبد الله عليه السلام يقول إن أشد ما يكون عدوكم (كراهة) (كراهته) لهذا الامر إذا بلغت نفسه هذه وأشد ما يكون أحدكم اغتباطا به إذا بلغت نفسه هذه - وأشار إلى حلقه - فينقطع (فتقطع) عنه أهوال الدنيا وما كان يحاذر عنها (فيها) ويقال له: امامك رسول الله صلى الله عليه وآله وعلى والأئمة عليهم السلام

Narrated through a chain of reliable/trustworthy narrators that Abu Abd-Allah Imam Sadiq (عليه السلام) said,

"The most intense state in which your enemy can happen to be in while hating this matter (i.e., Wilayah) is when his soul reaches here (throat), and the most intense state of happiness/delight in which one of you (Shias) can happen to be in is when his soul reaches here – and the Imam gestured to His throat – Then the horrors of the world will be cut off from him, and what he used to be wary/afraid of in the world. And it would be said to him, "In front of you is the Prophet of Allah (صلى الله عليه وآله), and Ali (عليه السلام), and the Imams (عليهم السلام)."

[Source: Kitab al-Zohad, Pg. 84, Hadith. 224]

Hadith 2:

حماد بن عيسى عن حسين بن المختار عن أبي بصير عن أبي عبد الله عليه السلام أنه قال: إن المؤمن إذا مات رأى رسول الله صلى الله عليه وآله وعليا عليه السلام بحضرته

Narrated through a chain of reliable/trustworthy narrators that Abu Abd Allah Imam Sadiq (عليه السلام) said,

"Verily the dead when he dies sees the Prophet (صلى الله عليه وآله) and Ali (عليه السلام) in his presence."

[Source: Kitab al-Zohad, Pg. 84, Hadith. 225]

Hadith 3:

محمد بن يحيى، عن أحمد بن محمد بن عيسى، عن ابن فضال، عن يونس بن يعقوب، عن سعيد بن يسار أنه حضر أحد ابني سابور وكان لهما فضل وورع و إخبات فمرض أحدهما وما أحسبه إلا زكريا بن سابور قال: فحضرته عند موته فبسط يده ثم قال: ابيضت يدي ياعلي، قال: فدخلت على أبي عبدالله (عليه السلام) و عنده محمد بن مسلم قال: فلما قمت من عنده ظننت أن محمدا يخبره بخبر الرجل فأتبعني برسول فرجعت إليه فقال: أخبرني عن هذا الرجل الذي حضرته عند الموت أي شئ سمعته يقول؟ قال: قلت بسط يده ثم قال: ابيضت يدي ياعلي، فقال أبوعبدالله (عليه السلام): والله رآه، والله رآه، والله رآه.

Narrated by Muhammad bin Yahya, from Ahmad bin Muhammad bin Isa, from Ibn Fazzal, from Younus bin Yaqob, from Saeed bin Yasir:

That I was there when one of the sons of Ibn Saaboor, who was a pious and great man, was ill, and i think his name was Zakariya bin Saabor, so at the time of his death, he extended his hand, and said, "You have enlightened my hand O Ali!"

The Narrator said, when I met Abi Abdillah (as) and Muhammad bin Muslim was also with him.

He (narrator) said: when I stood up from him, I believe mohammad bin muslim had told him about that man. So his Messenger came and I went with him to him.

Imam (as) said, "Tell me about this man with whom you were at time of his death, what did you hear? He said: I said he extended his arm and said that you have enlightened my hand O Ali.

So Abi Abdillah (as) said: By God! He saw Him, By God! He saw Him , By God! He saw Him.

[Source: Al-Kafi, Vol. 3, Pg. 131]

Narration is Realiable as per chain of narrators. See Mirat-Al-Uqool - Allama Majlisi, Vol. 13, Pg. 289

Hadith 4:

أخبرنا محمد بن محمد، قال: أخبرنا أبو القاسم جعفر بن محمد بن قولويه، قال: حدثنا أبو علي محمد بن همام، قال: حدثنا علي بن محمد بن مسعدة، قال: حدثني جدي مسعدة بن صدقة، قال: سمعت أبا عبد الله جعفر بن محمد (عليهما السلام) يقول: والله لا يهلك هالك على حب علي (عليه السلام) إلا رآه في أحب المواطن إليه، والله لا يهلك هالك على بغض علي (عليه السلام) إلا رآه في أبغض المواطن إليه

Narrated that Abu Abd-Allah Jafar bin Muhammad (عليه السلام) said,

"By Allah (عز وجل), the one who loves Ali ibn Abi Talib (عليه السلام) does not dies until he sees Him in the places most beloved/desirable to him. And by Allah (عز وجل) the one who hates Ali ibn Abi Talib (عليه السلام) does not die until he sees Him in the places most hateful to him"

[Source: Amaali - Sheikh Tousi, Pg. 164]

Hadith 5:

مُحَمَّدُ بْنُ يَحْيَى عَنْ أَحْمَدَ بْنِ مُحَمَّدٍ عَنْ عَلِيِّ بْنِ الْحَكَمِ عَنْ مُعَاوِيَةَ بْنِ وَهْبٍ عَنْ يَحْيَى بْنِ سَابُورٍ قَالَ سَمِعْتُ أَبَا عَبْدِ الله (عَلَيْهِ الْسَّلام) يَقُولُ فِي الْمَيِّتِ تَدْمَعُ عَيْنُهُ عِنْدَ الْمَوْتِ فَقَالَ ذَلِكَ عِنْدَ مُعَايَنَةِ رَسُولِ الله (صلّى اللهُ عَلَيْهِ وَآلِه) فَيَرَى مَا يَسُرُّهُ ثُمَّ قَالَ أَ مَا تَرَى الرَّجُلَ يَرَى مَا يَسُرُّهُ وَمَا يُحِبُّ فَتَدْمَعُ عَيْنُهُ لِذَلِكَ وَيَضْحَكُ

Narrate through a chain of reliable narrators that Abu Abd-Allah Imam Sadiq (عليه السلام) said:

“Regarding a dying person his eyes shed tears at the time of death. Then the Imam said, “This happens when seeing the Messenger of Allah (صلى الله عليه وآله), so he sees that which makes him happy. Don’t you see that when a person sees that which makes him happy his eyes shed tears while he laughs.”

[Source: al-Kafi, Vol. 3, Pg. 133]