The Electorial Commission site, which is more authoritative than the first reference I found, actually gives eligibility as:
So, again, the definition of a British Citizen post independence is relevant.a British citizen, an eligible Commonwealth citizen or a citizen of any other member state of the European Union.
Also, if Scotland fails to remain in the EU, would a citizen of another EU state (e.g. Spain) still be allowed to stand for the Scottish government?
Again, a statement made as to what will be the case when Scotland's situation post independence is still unknown.