ζέω + ὅλος
English translation (word)
zeō + holos
English translation (etymon)
to boil + whole
Epimerismi in Psalmos p. 140
T. Gaisford, Georgii Choerobosci epimerismi in Psalmos, vol. 3, Oxford, 1842
Ζηλῶ, παρὰ τὸ ζῆλος, τοῦτο παρὰ τὸ ζέειν ὅλος, ζέελος καὶ ζῆλος
Zēloō "to be jealous": from zēlos "jealousy, zeal", and the latter comes from "to boil" (zein) entirely (holos), *zeelos and zēlos
Choeroboscus, Epimerismi in Psalmos p. 158 (ἐζήλωσα, ἐκ τοῦ ζηλῶ, τοῦτο ἐκ τοῦ ζῆλος, τὸ δὲ παρὰ τὸ ζέειν ὅλως, παρὰ τὸ ὅλον κατὰ τὴν ἀντίφρασιν, τὸ μὴ ὂν σῶον); ibid., p. 163 (παρὰ τὸ ζέειν ὅλως); Etym. Gudianum, zeta, p. 231 (Ζῆλος, παρὰ τὸ ζέειν ὅλος, ζέελος, καὶ κράσει τῶν δύο εε εἰς η ζῆλος. τοῦτο παρὰ τὸ ζέω ζέηλος καὶ ζῆλος); ibid., chi, p. 562 (Χαμαίζηλος, παρὰ τὸ χαμαὶ καὶ τὸ ζῆλος, τοῦτο παρὰ τὸ ζέειν ὅλως)
Within Greek, ζῆλος belongs with ζητέω "to seek", δίζημαι "to pursue", but the connection was lost in synchrony. PIE root *i̯eh2- "pursue" (Beekes, EDG)
Persistence in Modern Greek
In Modern Greek ζήλος is still used to designqte the fervent derire for realizing something, but also the actions that someone takes in order to achieve a purpose.
Etymology parsing the word as a compound, identifying the second element as the adjective ὅλος, which is meant to account for the [lo], left unaccounted for in the older explanation following the derivational principle ζῆλος / ζέω. A contraction between the two vowels is assumed to yield the long vowel η, with first a change (unexplained) of [o] to [e]. The second element appears now as the adjective ὅλος, now as the adverb ὅλως, both being pronounced in the same way in Byzantine Greek.