Failing to provide factual evidence is not the same as equivocation, that would be a assertion, specifically one without basis.

Actually, if you read the OP rules, it is the same as equivocation.
Equivocating is rather more subtle, and involves manipulating the lexical semantics of the language to avoid an unambiguous answer. An example of equivocation, via the Oxford American Dictionary:
In the above example, both parties have the same understanding of the statement "take care of the taxes," but one party is taking advantage of the inherent ambiguity in the statement to feign truthfulness.
That is equivocation.

Equivocate:
e•quiv•o•cate - to speak vaguely or ambiguously, especially in order to mislead:
1- No equivocations on the questions, or to the questions!
2- No time wasting or side tracking to divert from the questions (i.e. tangents, or rabbit trails).
3- If you don’t know, simply say “I don’t knowâ€Â! But, understand, in saying so, you give up all right to say (for example) “there is no Godâ€Â; because you said “I don’t knowâ€Â. This includes making statements like (for example) “there is no evidence for God, therefore there is no God†because; you said “I don’t knowâ€Â. If you do attempt such, you are equivocating.
4- If you are going to make a “Negative†assertion without factual evidence for said assertion, you are equivocating.
5- If you are going to make any assertions to support your argument, insure they are factual assertions, not simply opinion. Otherwise you are equivocating.
6- Any assertions that do not deal directly with the questions are either equivocating or time wasting.
7- If you post links to other people’s opinions (regardless of their scholarship) without factual supporting evidences for said opinion, you are equivocating (and so were they).
Opinions are fine if they can be backed up by facts, but equivocations will not be allowed.