Considering desirable qualities is a much more open ended question but interestingly is often never considered. This is perhaps because committees rarely recruit for a trustee with particular qualities except in certain circumstances (see below). And in situations where a membership votes on the committee then it is for the members to decide who is a desirable candidate (which may be for a whole variety of reasons none of which are concerned with how well that person can operate on a committee). The third reason is that the true qualities required (collective decision making, wise judgment, clear foresight) are extremely difficult to measure and consequently difficult to overtly recruit for.
The commonest situation where committees do recruit looking for a particular skill is in the case of Treasurer (looking for finance/accounting skills).