May I direct readers initially to the OED in relation to 'twink', the simple stem of 'twinkle':
▪ II.twink, n.1
Forms: 5 twynk, 5–6 twynke, 6–7 twinke, 7 twinck(e, 7 twinch, 6– twink.
[f. twink v.1]
- A winking of the eye; transf. the time taken by this; a twinkling; now always in phrase in a twink; formerly at, in, with (a or the) twink of an eye; also with a twink; in the twink of a bedstick: cf. bedstaff.
14.. Cov. Corp. Chr. Plays i. 506 Myne enmyis to vanquese.. And with a twynke of myn iee not won to be lafte alyve. 1471 Ripley Comp. Alch. Pref. ii. in Ashm. Theatr. Chem. Brit. (1652) 127 In twynke of an Eye most sodenly. 1556 J. Heywood Spider & F. lii. A a iv. (heading), Wherat with twynke of an iye (as it were) the head spider..hath builded a strong castell in that copweb. Ibid. xci. Oo iv b, Change (by chance) brought him (at twinke of an iye) From twig top of the tree, at the rote to lie. 1561 Norton & Sackv. Gorboduc iv. ii. (Shaks. Soc.) 142 A pereles prince..Euen with a twinke a censeles stocke I sawe.
According to the OED the verb 'twink' also has long usage:
▪ IV.twink, v.1
Forms: see twink n.1
[ME. twinken (= MHG. and G. zwinken to wink), repr. the simple stem from which twinkle v.1 is formed.]
intr. To wink, to blink. Obs. c 1400 Gamelyn 453 Whan I twynke [v.r. twynk] on the, loke for to goon. c 1440 Promp. Parv. 505/2 Twynkyn, wythe the eye.., conniveo. 1600 J. Lane Tom Tel-troth 262 Some winke, some twinke, some blinke, some stare. a 1652 Brome Covent-Garden iii. i. Wks. 1873 II. 47, I will..set mine eye against his, that he shall not twink, but I'le perceive it. 1681 W. Robertson Phraseol. Gen. (1693) 567 To wink or twink with the eye, nictare.
To twinkle, sparkle. 1637 N. Whiting Albino & Bellama 3 The curled tapers of the Firmament Did cease to twinke. 1795 Cicely of Raby I. 195 The last star had twinked in the west, ere we had gone half our journey. 1856 Aird Poet. Wks. 194 The wings of birds Twink with illumination. 1884 Browning Ferishtah, Cherries 80 Like yon blue twinkle, twinks thine eye, my Love. 1896 C. K. Paul tr. Huysman's En Route iv. 54 Durtal faintly saw..stars twinking in the air.
Hence ˈtwinking vbl. n. 1519 W. Horman Vulg. 27 Ouermoche twyngynge [sic] of the yie betoketh vnstedfastnesse. 1627 May Lucan vi. 863 The eyes with twincking hard Are op'd.
Now compare 'wink' from the OED:
▪ V.wink, v.1
Forms: 1 wincian, 3 winken, 4–6 wynk(e, 4–7 winke, winck, 6–7 wincke, (4 Sc. vynk, 5 wynkyn, pa. tense wanke, wonk, 6 wynck(e, 9 pa. tense and pa. pple. wunk), 4– wink.
[OE. wincian wk. vb. = OS. wincon to nod, MLG., MDu. winken, related to OHG. winchan str. vb. (MHG., G. winken) to move sideways, stagger, nod; cf. OHG. winch (MHG. winc, G. wink) m. nod, OE. wince winch n.1: f. Teut. wiŋk-, older weŋk-:—Indo-Eur. weŋg-.
Other formations on the base wiŋk- (weŋk-): waŋk-:—weŋg-: woŋg-, to move sideways or from side to side, are OHG. wanc, wanch, MHG. wanc turning, return, instability, OS., OHG. wankôn (MLG., MDu., MHG. wanken); OHG. wenkan, OS. wenkean to waver, vacillate (MLG., MDu., Du. wenken to nod), whence OF. guenchir winch v.1; Lith. véngiu to do unwillingly, avoid, vangùs inactive, vìngis m. bend, curve, Albanian vank (vang-) felloe. See also wankle a., wenchel.
Examples of a strong conjugation in English (pa. tense wank, wonk) are very rare. The modern pa. tense and pple. wunk are jocular.]
- a. intr. To close one's eyes. (Also in fig. context: cf. 5, 6.) Obs.
c 897 ælfred Gregory's Past. C. xxxix. 287 Se stæpð forð mid ðam fotum & wincaþ mid ðæm eaᵹum [orig. oculos claudit]. c 1000 ælfric Gram. xxvi. (Z.) 156 Ic winciᵹe, conniueo. a 1225 Ancr. R. 288 Hwon þe heorte draweð lust into hire, ase þing þet were amased, & foð on ase to winken & forte leten þene ueond iwurðen. c 1374 Chaucer Troylus iii. 1537 Al for nought he may wel lygge and wynke But slep ne may þere in his herte synke. c 1386 ― Nun's Pr. T. 486 He wolde so peyne hym, that with bothe hise eyen He moste wynke, so loude he wolde cryen. Ibid. 611 For he that wynketh whan he sholde see, Al wilfully god lat him neuere thee. 1390 Gower Conf. I. 54 For ofte, who that hiede toke, Betre is to winke than to loke. c 1480 Henryson Two Mice 333 Quhylis wald he lat hir rin vnder the stra; Quylis wald he wink, and play with hir buk heid. c 1500 in Rel. Ant. I. 289 Sore me for-thinked, that I so moche wynked, For had I never more nede than nowe for to loke. a 1542 Wyatt in Tottel's Misc. (Arb.) 57 For cause your self do wink, Ye iudge all other blinde. 1562 [see winking ppl. a. 1]. 1584 Lyly Campaspe v. iv. 4 Though I winke, I sleepe not. 1611 Shakes. Cymb. v. iv. 194 There are none want eyes, to direct them the way I am going, but such as winke, and will not vse them...
This entry from Freidrich Kluge's 1891 'An Etymological Dictionary of the German Language' might also be of interest:
I leave it to others to respond to the OP's question.