I've wondered for years where the Korandjé verb wəy "gather (firewood)" comes from. It normally appears in the idiom a-wwəy-ts skudzi [3Sg-gather-hither wood] "she gathered in firewood". On p. 333 of Heath's grammar, I found the explanation, in the following example:
[He] has brought firewood here.
The Tamasheq verb in question, awəy in the imperative, is simply the normal Berber word for "take, bring" (which in Korandjé is expressed with a Songhay verb, zəw), so I would have hesitated to connect them based on a dictionary entry alone. But given this attested usage with "firewood", the semantic specialisation poses no problems. What does surprises me is that it was borrowed as a bare stem, rather than with a fossilised 3rd person prefix y/i - contrast yəf (Tashelhiyt y-arf "roast", not attested in Tamasheq), ikna "make" (Tamasheq i-kna). Usually, only stems that start with a syllabic onset are borrowed into Korandjé without the y/i.
Another probable loan into Korandjé that I noticed going through the grammar is Korandjé ləwləw "shine, gleam" - cp. Tamasheq m̀ələwləw "shine".
However, a number of words have gone the other way - from Songhay into Tuareg. Heath comments on many of these in his dictionary (eg kə̀rikəw "practice sorcery"), but not all. One that struck me is the verb ḍùkr-æt "become angry at", obviously related to Gao Songhay dukur "be angry"; I don't recall seeing this verb elsewhere in Berber (not even in Alojaly's dictionary of Tamajeq), whereas it's widespread in Songhay.
Obviously cognate are Tamasheq é-tæqq "male ostrich" and widespread Songhay forms such as Gao taatagey, Fulan Kirya taataɣey "ostrich" (the shift of g to ɣ next to non-high back vowels is regular in several Songhay varieties, and in Tamasheq qq is the geminate equivalent of ɣ). The word is generic in Songhay but specific in Tuareg - the opposite of what we saw with "bring" - which suggests to me that it was borrowed into the latter, as does the fact that I don't find the term in Alojaly's Tamajeq dictionary. However, since ostriches are extinct in most Berber-speaking areas, it's difficult to prove the direction of borrowing.