Slowly poking around digitized back issues of Studia Orientalia, I recently ran into Kecskeméti (1968), an article indexing Pallas‘ Zoographie (1811). This is a notable early source of animal names from several languages of Russia, collected since the late 1700s. Some of these languages would not be otherwise substantially attested until the 1900s, and for a few it is just about the last source available before extinction. (Pallas’ consistency in transcription and coverage are both poor, but we’ll take what we can get.)
During a closer look, for checking some Samoyedic data, I however had to do a double-take upon reaching the heading Mᴇsᴛsᴄʜᴇʀᴀᴇᴄɪs. This is obviously Meshcheran, one of the extinct more western Uralic languages. (Interestingly also with /-sč-/ and not the evidently Russified /-šč-/?) Except, all sources I have seen so far have claimed that Meshcheran went extinct already somewhere around the 1500s…
OK, Pallas only records four “Mestscheraic” words, and a distinct Meshcheran ethnicity is reported to have lingered long after Russification — in at least one case even into the current century!  So fairly likely we are dealing here not with a living language, only with substrate loan vocabulary, a natural enough fate for animal names. Yet this is still interesting due to being an attestation securely flagged as Meshcheran. There are two competing theories on the affinity of this language within Uralic — one sees it as a branch or sister of Mordvinic, the other, Permic. To my knowledge both of these build mainly on evidence such as toponymy found in the traditionally Meshcheran region, which is susceptible to errors from pre-Russification population movements.
The list comprises bird names entirely, all given with obsolete binomials:
- Büdaenae ‘Tetrao coturnix’ (= hazelhen, Coturnix coturnix)
- Kagau ‘Accipiter milvus’ (= red kite, Milvus milvus)
- Kuki ‘Cuculus borealis’ (= a cuckoo sp., probably the common cuckoo Cuculus canoris)
- Schibirtschik ‘Motacilla albeola’ (= common wagtail, Motacilla alba)
The third is obviously undiagnostic of anything, but the others may be worth something.
I cannot make much of the first on a quick lookaround: it would be a hard match for the common Mordvinic term for the hazelhen (Erzya /povo/, Moksha /pova/ < PU *püŋə) and even poorer for the common Permic term (Udmurt /śala/, Komi /śɤla/) — at most it has some very vague similarity to Komi /bajdɤg/ ‘partridge, tarmigan’.  The second is however a good match with Mordvinic /kaval/ ‘kite’ (? < *kaɣal), though the implied vocalization of final *-l meanwhile looks amusingly Permic. The last has vague and probably insufficient similarity with Moksha /šäjgiča/ ‘wagtail’ (← /šäj/ ‘valley’ + /kiča/ ‘gull’) on one hand, Russian шибать ‘to hit’ (< Proto-Slavic ‘to whip’) on the other.
I do not feel like rooting around for possibly related names of similar birds; but per ‘kite’ I would at this point lean cautiously towards a Mordvinic-ish affiliation for Meshcheran.
 In a blog post this short you’ll probably manage without me doing hyperlinks for the footnotes.
 Thus per V. Patrušev apud Rahkonen (2009) in a single village “in a Mordvin area”.
 This is probably a loan from early Hungarian or some common source though — cf. Hu. fajd ‘grouse’, from earlier #paďt- per Mansi *paľta ‘black grouse’. If this really were a common Uralic root, I would expect instead **poľt- in Permic (and the cluster *-ďt- would be also unprecedented). OTOH Komi seems to show *p-d > /b-d/, which may allow dating the word to the common Permic era regardless.