Is the letter U (whether spelled as U or V) between NG and a vowel always a consonant? It is at the very least a useful rule of thumb, but I wonder if there are counterexamples to this rule (or tendency). The main examples that come to mind are lingua and sanguis and pinguis and unguis, all bisyllabic, where U is a consonant. Does it perhaps depend on which vowel follows or do the surroundings not help detect counterexamples?
Practically always, but not in relangŭit in the poetry of Ovid
The sequence "NGV" + vowel letter is only found in a small number of words plus their derivatives. The pronunciation is nearly always non-syllabic, analyzed either as /ngw/ or /ngʷ/ depending on your theoretical preferences. I prefer /ngw/. (Technically, there are other possible analyses like treating V+the following vowel as a rising diphthong, or treating V as a non-syllabic vowel [u̯] instead of a consonant phoneme /w/, but I haven't seen recent treatments that advance either of those analyses for Classical Latin.)
Syllabic u occurs in the perfect (but not the present) stem of the verb languēscō and its derivatives such as relanguēscō according to Lewis and Short. Using PHI Latin word seach, I found these two examples of forms ending in langŭit in Ovid:
"inposito fratri moribunda relanguit ore" (Metamorphoses 6.290-291)
i͞npŏsĭ|tō frā|trī morĭ|bu͞ndă rĕ|la͞ngŭĭ|t‿ōre;
"cum bene pertaesum est, animoque relanguit ardor" (Amores 2.9b.27)
cu͞m bĕnĕ |pe͞rta͞e|su͞m‿est,‿ănĭ|mōquĕ rĕ|la͞ngŭĭ|t‿a͞rdor
(Macrons used here to mark heavy syllables, not long vowels; feet separated with |)
In constrast, the langues- of the present stem scans as two heavy syllables in the four places where it occurs in Ovid (Amores 2.10.35, Metamorphoses 8.523, Fasti 2.775, Tristia 3.3.39).
Explanation of the syllabic U in relanguit
I think there might be an etymological or morphological explanation for the syllabic -u- in this context. I have a vague memory of Manu Leumann saying in Lateinische Laut- und Formenlehre that the perfect ending -uī in Latin verbs of the second conjugation developed from an earlier sequence containing the vowel e, like *-eui/evi; unfortunately, I don't have access to this work right now, so I can't check for the citation or the details of the derivation (for example, I don't know how the e here would get to be short instead of long). Anyway, if this is correct, it might be that langŭ- in langŭit is a simplification of some earlier sequence like langʷeu- where some form of *-e- originally intervened between the labial(ized) consonant at the end of the root and the labial perfect suffix -u-/-v-.
Similarly, Lewis and Short shows alternation between -qu- in the present stem and -cu- in the perfect stem for liquēscō, licŭī and its prefixed forms. For example, Ovid uses the form "dēlĭcŭit" (Metamorphoses 4.253, 7.381, Tristia 3.10.15).
Given the rarity of /ngu/ before a vowel and the apparent lack of minimal pairs between /ngw/ and /ngu/, the scansion of -ngui- as -ngŭi- in the two lines above could perhaps be interpreted as a case of poetic diaeresis where /u/ stands for /w/, an explanation found in The Principles of Latin Grammar, by Peter Bullions (1851) (page 300) and Adam's Latin Grammar by Allen Fisk (1833) (page 186). However, An elementary manual of Latin prosody by William Ramsay (1859), specifically says that relangŭit is always four syllables (page 69), and so is not analogous to poetic pronunciations like silŭa where the word had a Classical Latin pronunciation with non-syllabic -v-.
I'm inclined to agree with Ramsay. Non-syllabic -qu- and -gu- have often been analyzed as unitary phonemes /kʷ/ and /gʷ/ (although that phonemic analysis is arguable for Classical Latin). I feel like they would not alternate with a consonant-vowel sequence as easily as the sequence /lw/ (which I believe often derived in Latin from an earlier /lu/ or /l/ + vowel + /w/ sequence—a comment by Alex B. says that original /lw/ is supposed to have changed in Latin to /ll/). And I am not aware of any word that displays variable scansion between /ngw/ and /ngu/: as far as I know, all other words spelled with "NGV" + vowel letter always scan with /ngw/. Surprisingly, however, there are some alleged cases of diaeresis of -qu- to -cu- [ku] in poetry—I've asked a separate question to try to study these in more depth.
No other examples that I know of
I'm not sure if there are any other verbs that can have a perfect stem ending in /ngu/ with syllabic /u/, but it seems not. Here are possible candidates and my research so far:
Langueo is the only second-conjugation verb ending in -ngueo. Aside from languēscō and its derivatives, there seems to be one other inchoative third-conjugation verb ending in -nguēscō: pinguēscō (along with prefixed compinguēscō). However, there seem to be no attested perfect forms for (-)pinguēscō.
Ung(u)o: Dictionaries treat it as a variant of ungo with the same perfect stem, unx-. There are hits in PHI for ungui but I can't tell whether any are a perfect form; it exists separately as the present passive infinitive form of unguo and as a form of unguis, both of which would be pronounced with /ngw/.
Stinguo is rarely used unprefixed. The prefixed forms distinguo, ex(s)tinguo have perfect stems ending in -tinx- according to Lewis and Short. These verbs have passive infinitives in -nguī and present third-person singular forms in -nguit, which makes it difficult to search for any possible alternative perfect forms in -u-.