These are surprisingly difficult lines to translate; often the apparently simple things are. And I am not happy with my current translation; it is more of a hypothesis at this point, and I am already wanting to change it.
To briefly address your question: in SN 48.54, I assume you’re referring to the phrase padāni bodhāya saṃvattanti. Here, pada governs the verb and is hence nominative.
The phrase amataṁ padaṁ may often be in accusative, for example at Thag 16.10:
phuseyya amataṃ padaṃ.
One may realize the deathless state.
In Dhp 21, however, there is no verb, and in such constructions we normally infer hoti:
appamādo amatapadaṁ hoti
Diligence (is) the deathless state.
Now, as to the meaning of the words, this where things get tricky.
The phrase occurs 7 or 8 times in the suttas, always in verse. Given that amata is an important term for the Vedas, this strongly implies that the memory of Vedic verse is still retained in this phrase. In other words, it is probably a re-definition of the Vedic idea of amṛta, “immortality”, also the “nectar of the gods (that confers immortality)”.
Given that it is poetic, we should avoid pressing the technical meaning too far.
The obvious reading is that amata is Nibbana, and this is indeed how it is glossed usually in the commentaries. However the suttas don’t necessarily support this. In Thig 13.3 the amatapada is said to be the four noble truths. This is indirectly supported at Thig 6.4, where the realization of the amatapada is stream entry, normally asscociated with seeing the four noble truths. The commentary to Iti 62 backs this up: anamatagge saṃsāre anaññātaṃ anadhigataṃ amatapadaṃ catusaccadhammameva vā jānissāmi.
Pada is often translated as “path”, and the entry in the PTS dictionary gives this as a meaning. Also the commentary to this verse glosses pada as magga, upāya. However there doesn’t seem to be much support for this, and the entries given for this meaning in the dictionary are not persuasive. Nor does there seem to be support for this sense in Sanskrit. Modern translators (Norman, Anandajoti) thus tend to reject this sense. Certainly if the amatapada is Nibbana then pada cannot mean “path”.
Possible meanings of pada include:
- “mark, characteristic”, following from the sense of “footprint”, or as we might say, “fingerprint”. See for example, the tathāgathapadāni, the “footprints of the Realized One”, i.e. the jhanas. This is the place the Buddha has walked and we can see the signs.
- “state” or less persuasively Norman’s “place”. This is the common rendering these days.
- “word” or 'saying". Perhaps a left-field entrant, but amatapada is usually used with the verbs phusati “realize, experience”, or deseti “teach”.
A further ambiguity comes with maccu, “death” or commonly “Death”, i.e. the embodiment of death the “King of Death”. Thus we could have:
Diligence is the deathless teaching;
negligence is the teaching of Death.
More likely, though, we should understand pada as “state”, as the second half of the verse implies.
One possibility would be to read both amata and maccu in personal terms:
Diligence is the state of the Immortal;
negligence is the state of Death.
However amata is not really attested in Pali in this way, i.e. as an epithet of the Buddha. Thus we
Diligence is the deathless state;
negligence is the state of death.
The underlying issue with the verse is that diligence, while of course always a good thing, is not really equivalent to Nibbana. This is why, I believe, the commentary and later translators assume it must mean “path”. So why are these two ideas associated in this way?
Well, it’s poetry. The word we translate as “diligence” is appamāda, the negative of pamāda, from the root mada, “intoxication, pride, madness”. You don’t have to look too hard to see a play on mada and mata. Or as we might say in English “dead drunk”.
So it seems to me the play is that based on the idea that those who are drunk or intoxicated are asleep or as if dead, while those who remain bright and alert are in the state of those who are “not-dead” i.e. “awakened”. Pamāda really straddles the boundary between “trying, effort” and “alert, conscious”. The rendering “negligence” puts the stress on the former part, but here it seems the stress should be on the latter.
Freely translating this sense:
One is not dead is alert and conscious;
unawareness is the state of death.
More literally, and reverting to the standard renderings of pamāda/appamāda:
Heedfulness is the deathless state;
heedlessness, the state of death.
Compare the lines I have rendered as:
Diligent among the negligent,
wide awake while others sleep
Here too the rendering would be better as:
Heedful among the heedless,
wide awake while others sleep