I was wondering when MacBain would be mentioned. Always wise to seek "a second opinion" in relation to the etymologies therein. Having siad that, many of them are correct and an ON antecedent of "both" would be of no surprise. As said previously, Vendryes (in French, paperback, many vollumes) is still the man in this area and it really is time a team-production historical dictionary of both Gaelic languages was available. (Its coming! Its coming!)

I don't want to send those with a casual interest in the wrong direction either -

MacBain the only accessible dictionary of that type available and most of it is grand. Just that you won't know when it is dangerous.

Vendryes - not for the casual browser. Mainly concerned with etymologies (Indo-European roots etc.) of Old Irish forms, therefore not dealing with forms of words likely to occur in current songtexts.