Probably from the same as pale (through the idea of oscillatory repetition); (adverbially) anew, i.e. (of place) back, (of time) once more, or (conjunctionally) furthermore or on the other hand -- again.

see GREEK pale

1. anew, again (but the primary meaning seems to be back; cf. (among others) Ellendt, Lex. Sophocles, under the word, ii, p. 485);

a. joined to verbs of all sorts, it denotes renewal or repetition of the action: Matthew 4:8; Matthew 20:5; Matthew 21:36; Matthew 22:1, 4; Mark 2:13; Mark 3:20; Luke 23:20; John 1:35; John 4:13; John 8:2, 8, 12, 21; John 9:15, 17; John 10:19; Acts 17:32; Acts 27:28; Romans 11:23; 1 Corinthians 7:5; 2 Corinthians 11:16; Galatians 1:9; Galatians 2:18; Galatians 4:19; 2 Peter 2:20; Philippians 2:28; Philippians 4:4; Hebrews 1:6 (where πάλιν is tacitly opposed to the time when God first brought his Son into the world, i. e. to the time of Jesus' former life on earth); Hebrews 5:12; Hebrews 6:1, 6; James 5:18; Revelation 10:8, 11; πάλιν μικρόν namely, ἔσται, John 16:16f, 19; εἰς τό πάλιν, again (cf. German zum wiederholten Male; (see εἰς, A. II. 2 at the end)), 2 Corinthians 13:2; with verbs of going, coming, departing, returning, where again combines with the notion of back; thus with ἄγωμεν, John 11:7; ἀναχωρεῖν, John 6:15 (where Tdf. φεύγει and Griesbach omits πάλιν) (cf. John 6:3); ἀπέρχεσθαι, John 4:3; John 10:40; John 20:10; ἐισέρχεσθαι, Mark 2:1; Mark 3:1; John 18:33; John 19:9; ἐξέρχεσθαι, Mark 7:31; ἔρχεσθαι, John 4:46; John 14:3; 2 Corinthians 1:16; 2 Corinthians 12:21 (cf. Winers Grammar, 554 (515) n.; Buttmann, § 145, 2 a.); ὑπάγειν, John 11:8; ἀνακάμπτειν, Acts 18:21; διαπεραν, Mark 5:21; ὑποστρέφειν, Galatians 1:17; ἡ ἐμή παρουσία πάλιν πρός ὑμᾶς, my presence with you again, i. e. my return to you, Philippians 1:26 (cf. Buttmann, § 125, 2); also with verbs of taking, John 10:17; Acts 10:16 Rec.; .

b. with other parts of the sentence: πάλιν εἰς φόβον, Romans 8:15; πάλιν ἐν λύπη, 2 Corinthians 2:1.

c. πάλιν is explained by the addition of more precise specifications of time (cf. Winer's Grammar, 604 (562)): πάλιν ἐκ τρίτου, Matthew 26:44 (L Tr marginal reading brackets ἐκ τρίτου); ἐκ δευτέρου, Matthew 26:42; Acts 10:15; πάλιν δεύτερον, John 4:54; John 21:16; πάλιν ἄνωθεν, again, anew (R. V. back again (yet cf. Meyer at the passage)), Galatians 4:9 (Wis. 19:6; πάλιν ἐξ ἀρχῆς, Aristophanes Plutarch, 866; Plato, Eut., p. 11 b. and 15 c.; Isoc. areiop. 6, p. 338 (p. 220, Lange edition); cf. Winer's Grammar, as above).

2. again, i. e. further, moreover (where the subject remains the same and a repetition of the action or condition is indicated): Matthew 5:33 (πάλιν ἠκούσατε); Matthew 13:44 (where T Tr WH omit; L brackets πάλιν), ; ; Luke 13:20; John 10:7 (not Tdf.); especially where to O. T. passages already quoted others are added: Matthew 4:7; John 12:39; John 19:37; Romans 15:10-12; 1 Corinthians 3:20; Hebrews 1:5; Hebrews 2:13; Hebrews 4:5; Hebrews 10:30; Clement of Rome, 1 Cor. 15, 3f [ET] and often in Philo; cf. Bleek, Br. a. d. Hebrews 2:1, p. 108. 3. in turn, on the other hand: Luke 6:43 T WH L brackets Tr brackets; 1 Corinthians 12:21; 2 Corinthians 10:7; 1 John 2:8 (Wis. 13:8 Wis. 16:23; 2 Macc. 15:39; see examples from secular authors in Pape, under the word, 2; Passow, under the word, 3; (Ellendt as above (at the beginning); Liddell and Scott, under the word, III.; but many (e. g. Fritzsche and Meyer on Matthew 3:7) refuse to recognize this sense in the N. T.)). John uses πάλιν in his Gospel far more frequent than the other N. T. writings, in his Epistles but once; Luke two or three times; the author of the Rev. twice.