"I do not have another map."
Translation:Chan eil mapa eile agam.
No. eil comes from lenited fuil (old dependent form of tha) through fhuil (pronounced as uil) which changed to eil. If it were to be written etymologically, it’d be written *fheil. Also bheil (as in a’ bheil thu…?) comes from fuil, eclipsed to bhfuil, pronounced as bhuil, with the same vowel change to bheil (the mutation called eclipsis has since disappeared in Gaelic, but this word is its remnant).
eile on the other hand comes from Old Irish aile, eile meaning other, second.