v1.0
Publishing history:
v1.0: 01/10/24
gòcaireachd f. [see below], gen. idem., ‘fooling’. Henderson (1910, 210) considers SG gòcaireachd, with a long vowel, to be founded on ON gaukr m. ‘bungler, simpleton, blockhead’; 
The primary meaning of ON gaukr is ‘cuckoo’.
A. SG gogaireachd
A 1. SG gogaireachd [ˈɡ̊ɔɡ̊əɾʲəxk], -axk], -ɔxk] 
Or with [o].
A 2. SG gògaireachd [ˈɡ̊ɔːɡ̊əɾʲəxk], -axk], -ɔxk] 
Or with [oː].
A 3. SG gogmaireachd (CG VI, 85: ‘the work of a gouk, April fooling, mockery, teasing’).
B. SG gocaireachd
B 1. SG gocaireachd [ˈɡ̊ɔʰkəɾʲaxk], -ɔxk] 
Or with [o].
B 2. SG gòcaireachd [ˈɡ̊ɔːʰkəɾʲaxk], -ɔxk] 
Or with [oː].
Long ò of gòcaireachd is substituted with short o in the margin of the National Library of Scotland’s downloadable PDF copy˄ (ex libris Angus Matheson (1912–1962), Professor of Celtic, University of Glasgow 1956–1962) of Henderson 1910.
The usual form of this word appears to be (A 1) gogaireachd; the form (B 1) gocaireachd seems restricted to Lewis; (A 2) gògaireachd and (B 2) gòcaireachd, with their long stressed vowels, appear to be relatively late; (A 3) gogmaireachd is unexplained. SG gogaireachd appears to be based on SG gogaire, also gògaire, ‘a gouk [Scots gowk “fool”], a gawkerel [cf. Scots gomerel “fool”], a silly person, a person sent “a-gouking” on 1 April, an April fool’ (CG VI, 85), var. gogair ‘stupid fellow, fool’ (Dwelly 1911; 
Where it is ascribed to MMcD, which may be for Malcolm MacDonald of Stornoway. The abbreviation is not expanded in Dwelly’s dictionary, but is in his appendix (Dwelly App.).
ON gauk acc. would be expected to yield SG [ɡ̊ɔːɡ̊]-, which is unlikely to result in SG gog-, goc-, gòg- and gòc-, according to dialect, directly.
With its range of vocalisms, however, Scots gowk ‘cuckoo; fool’ (generally) [gʌuk], (Ulster) [gʌuk], [go:k] (SND˄), (Orkney) [gɔk] (Marwick 1929, s.v. gokk), (Shetland) [gɔk], [gåk], [gōək] (Jakobsen 1928, s.v. gok) might well account in Scottish Gaelic for alternation between short and long vowels (gogair(e) ~ gògaire, gogaireachd ~ gògaireachd), as well as the alternation between unpreaspirated and preaspirated velar plosives (gogaireachd/gògaireachd ~ gocaireachd/gòcaireachd). Further, the related Scots gowkmaleerie ‘giddy female’ (< gowk + ma + leerie 
With Scots ma ‘an intermediate syllable appearing frequently in Scots compound words, usually of obscure, imitative or ludicrous origin; it is apparently for rhythmic effect only’ + leerie ‘originally a meaningless word or element used for rhythmic purposes in children’s rhymes and as a suffix in such words as [gowkmaleerie] to denote sprightly, bustling motion, fanciful appearance or the like’ (SND˄).
It may well be, however, that in the first instance Scots gowk was adapted morphemically to SG gog in the sense ‘nod; tossing of the head’, which MacBain (1911) derives from Eng. cock, and which occurs as the adjectival element in SG gog-cheannach adj. ‘light-headed; giddy; with head shaking’, 
Shaw 1780: gogcheannach ‘light-headed, whole head shakes’; Mac Farlan 1795: ‘shaking of the head’; MacFarlane 1815: ‘light-headed’; Armstrong 1825: ‘giddy, light-headed, shaking or nodding the head in walking (as in deer)’; HSS 1828: gogcheannach ‘light-headed’; McAlpine 1832: ‘idem’; MacEachen 1842: ‘idem’; cf. Ir. gogaire in the sense ‘giddy person’ (Ó Dónaill 1977).
Faclan bhon t-Sluagh˄, Scalpay.
Mac Farlan 1795: ‘coquette’; HSS 1828: ‘light-headed woman, coquette’; AFB˄: ‘coquette, flirt, butterfly; light-headed/giddy woman’.
Armstrong 1825: ‘coquette, giddy female, stupid trull’; HSS 1828: ‘light-headed woman; coquette’; McAlpine 1832: ‘light-headed girl’; Dwelly 1911: ‘light-headed woman, coquette, giddy female, stupid trull’; MacLennan 1925: ‘light-headed girl, coquette’; AFB˄: ‘coquette, flirt, butterfly; light-headed/giddy woman’; cf. Ir. gogaide in the sense ‘giddy woman’ (Ó Dónaill 1977), ‘giddy person, a feeble old woman; [?and by extension] a midwife; the hunkers; a blow’ (Dinneen 1947).
Armstrong 1825: ‘silly female, stupid trull, coquette, doting female’.
MacFarlane 1815: ‘coquette, foolish woman’; Armstrong 1825: = gogail; cf. Ir. gogaille in the sense ‘goose’ (Ó Dónaill 1977).
Mac Farlan 1795: ‘coquetry’; MacFarlane 1815: ‘idem’; Armstrong 1825: ‘coquetry, female finesse, womanish stupidity’; HSS 1828: ‘light, airy behavour, coquetry’; McAlpine 1832: ‘giddiness’; MacEachen 1842: ‘light behaviour, coquetry’; Faclan bhon t-Sluagh˄: ‘excitement’.
Shaw 1780: gogailleachd ‘dotage’; Armstrong 1825: gogail(l)eachd ‘behaviour of a silly female, low coquetry, dotage’.
Potentially, then, when first borrowed into Scottish Gaelic, Scots gowk may have been adapted on the model of SG gog, but also yielding SG gòg, perhaps due to repeated exposure to long-vowel forms of Scots gowk, especially via association with April Fool’s Day, and/or influence from SG gòrach ‘foolish’; 
Cf. also gòrag f. ‘foolish woman’, gòraich f., gòraileis and gòrlais f., and gòrachas m. ‘folly’.
MacLennan (1925) makes a distinction between on the one hand SG gocaireachd ‘playing the fool on 1 April’, which (as noted above) he derives from Scots gowk, and on the other SG gogaireachd ‘loitering’. From this it appears that the form gogaireachd at least may incorporate a further loan-blend, from Scots gawk [′gǫ:k(e)], [′gɑ:k(e)] in the senses ‘to fool around, idle, wander aimlessly about’ (SND˄, s.v. 2gawk).