And Irish capall and Spanish caballo (since the /b/ and /v/ sound are merged there), and Italian cavallo and Portuguese cavalo, all presumaby from from the vulgar Latin caballus, whose root shows up in English "cavalry," "cavalier," and "cavalcade."
"Caballus" is actually a loan into Latin - most likely from an ancient Celtic language.https://en.wiktionary.org/wiki/caballus
There are some Celtic loans into Latin that were subsequently reintroduced in Irish and Welsh (and English!) rather than coming directly from proto-Celtic, such as "cloccus" (bell) > cloch, clóg, "clock", or "currus" (chariot, wagon) > car, carr, "car".
But ceffyl and capall look more or less the way you'd expect if they'd been retained from Proto-Celtic, rather than being loans from Latin. And the Romans took a lot of terminology relating to horses and transport from the Celtic languages.
I have a horrible habit of translating 'eisiau' as 'need.' Just for information, am I far wrong?
The GPC seems to think so - http://geiriadur.ac.uk/gpc/gpc.html?eisiau. It's translated as "want", "lack", "deficiency" and so on (bear in mind that it's a noun, rather than a verb). The course creators may have a preference for "want" though, to keep it separate from anghen (need).
On a side note, anghen is like eisiau in that it's a noun - so you don't put yn in front of it.