Mark,
We actually have zero qualifications to serve as Director on our Board. This of course means that you could serve as a Director in my Association (we have a vacancy if your interested

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I actually looked at having a qualifier that only members may serve. However, in gathering signatures I became educated in the issues of the day and chose to abandon that cause. It seems that we have a large number of elder persons in our area (or did at the time). Many of those were, due to financial reasons, simply living together vs. being married. Those that were on second marriages chose not to place their new spouse on the deed to the property (many said it kept peace with the children). Having a "members only" qualifier would have eliminated those spouses or significant others from serving.
You should also check the applicable State statutes to your Association. Some States have specified that an HOA/COA may not prohibit members from serving.
As to non-resident members serving on the Board - We have had several serve that lived within commuting distance. There were few problems having them serve and they contributed greatly. We have had a few Directors who became non-resident members outside the commuting distance who tried to serve but simply couldn't be counted on to do anything.
My Sister owns a house in Colorado that everyone on the Board doesn't live full time on the property. They work well together but only meet once a quarter.
I think it will depend on the size of the community, the responsibilities of the Association (upkeep of amenities, etc.) and the issues within the community (if everyone is paying assessments on time and plays nice together then there is little to no enforcement issues).