Sometimes it goes one step further, and psychosomatic changes become apparent:
Then Sariputta the wanderer went to Moggallana the wanderer. Moggallana the wanderer saw him coming from afar and, on seeing him, said, “Bright are your faculties, my friend; pure your complexion, and clear. Could it be that you have attained the Deathless?”
"Yes, my friend, I have attained the Deathless. " Mv 1.23.1-10
It takes various levels of “something of value” for a given person to think that “It works”, so these differ in that way.
For the non-religious samvega-experiencers, “something of value” doesn’t warrant a commitment to the religion in toto, such that “Buddhism works” doesn’t apply (and anyway, which one?). It’s a bit of an argument from authority, but religious people who agree with this approach to Founder/Church (= Sangha) statements call it “faith”.
The EBTs seem to say that mental calm comes from such a faith, but I wonder about the many modern folk for whom faith is not associated with mental calm…
AN5.77, AN5.78, AN5.79, AN7.80 are all to develop samvega:
"There is the case where a monk reminds himself of this: At present I am young, black-haired, endowed with the blessings of youth in the first stage of life. The time will come, though, when this body is beset by old age. When one is overcome with old age and decay, it is not easy to pay attention to the Buddha’s teachings. It is not easy to reside in isolated forest or wilderness dwellings. Before this unwelcome, disagreeable, displeasing thing happens, let me first make an effort for the attaining of the as-yet-unattained, the reaching of the as-yet-unreached, the realization of the as-yet-unrealized, so that — endowed with that Dhamma — I will live in peace even when old. AN5.79
To be certain -and go beyond doubt that it works, stream entry is doctrinally the best standard. This is called unshakable faith (aveccapasāda, if I am not mistaken). Pāsāda is ‘building’, is different and potentially shakable - especially if on stilts! I’m familiar with the Sinhalese version of this word meaning building, but the Pali term may have other meanings to it, in what kind of building it is.
There is a sutta where it is said that when a meditator attains the first jhana, faith arises (as well). In general less degrees of faith arises when practice reaps benefits.
The sutta below is interesting -it has both saddha and pasāda in the same sutta.
Yassa saddhā tathāgate,
Sīlañca yassa kalyāṇaṃ,
Saṅghe pasādo yassatthi,
Adaliddoti taṃ āhu,
amoghaṃ tassa jīvitaṃ.
Tasmā saddhañca sīlañca, pasādaṃ dhammadassanaṃ;
saraṃ buddhāna sāsanan”ti.
When one has faith in the Tathāgata,
unshakable and well established,
and virtuous behavior that is good,
loved by the noble ones and praised;
when one has confidence in the Saṅgha
and one’s view has been straightened out,
they say that one is not poor,
that one’s life is not lived in vain.
Therefore an intelligent person,
remembering the Buddhas’ teaching,
should be intent on faith and virtuous behavior, confidence and vision of the Dhamma. AN4.52
The meaning of Pasāda seems have several meanings- confidence, praise, delight (in a teacher or teaching), a clear mind, and finally faith. You might have researched this more and may have come across other meanings too.
Cakkhuppasāda means (abhidhammic term) perhaps the glow of awareness or the first stimulation of the eye door. This still contains this idea of glow, clarity, light, delight, joy-perhaps overlaps with nandi, and piti.
Passaddhi is a Pali noun (Sankrit: prasrabhi, Tibetan: ཤིན་ཏུ་སྦྱང་བ་,Tibetan Wylie: shin tu sbyang ba) that has been translated as “calmness,” “tranquillity,” “repose” and “serenity.” The associated verb is passambhati (to calm down, to be quiet).
In Buddhism, passaddhi refers to tranquillity of the body, speech, thoughts and consciousness on the path to enlightenment. As part of cultivated mental factors, passaddhi is preceded by rapture (pīti) and precedes concentration (samādhi).
Passaddhi is identified as a wholesome factor in the following canonical contexts:
the seven factors of enlightenment (sambojjhangas)
meditative absorptions (jhanani)
transcendental dependent arising (lokuttara-paticcasamuppada)