The long vowel is difficult to explain, but according to some authors it is an artifact of early simplification of the cluster *gdʰ in *teg-dʰlom (see -bulum for the suffix); compare rēgula. (Can this(+) etymology be sourced?) Contrast the later formation tegulum, with a short vowel.
Glires: isicio porcino, item pulpis ex omni membro glirium trito, cum pipere, nucleis, lasere, liquamine farcies glires, et sutos in tegula positos mittes in furnum aut farsos in clibano coques.
Dormice: Fill the dormice with minced meat of pork and all parts of the dormice, ground pepper, pinenuts, laser, fish-sauce, and put them sewn together and laid upon a tile-pan into the oven, or cook them stuffed in the clibanus.
De Vaan, Michiel (2008) “tegō, -ere”, in Etymological Dictionary of Latin and the other Italic Languages (Leiden Indo-European Etymological Dictionary Series; 7), Leiden, Boston: Brill, →ISBN, page 608
Further reading
“tegula”, in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
"tegula", in Charles du Fresne du Cange’s Glossarium Mediæ et Infimæ Latinitatis (augmented edition with additions by D. P. Carpenterius, Adelungius and others, edited by Léopold Favre, 1883–1887)
“tegula”, in Harry Thurston Peck, editor (1898), Harper's Dictionary of Classical Antiquities, New York: Harper & Brothers
“tegula”, in William Smith et al., editor (1890), A Dictionary of Greek and Roman Antiquities, London: William Wayte. G. E. Marindin
Schuchardt, Hugo (1918) Die romanischen Lehnwörter im Berberischen (Sitzungsberichte der Wiener Akademie der Wissenschaften; 188, IVth treatise) (in German), Wien: In Kommission bei Alfred Hölder, page 57
Tegula (insect anatomy) on Wikipedia.Wikipedia 
