Burn a Political Action card for no vote?

From the Rulebook ---

6.3.3. Gaining Votes

<snip>
Once gained, a vote need not be cast right away, if at all. Each vote cast is cast either "for" or "against" the referendum, ...
<snip>
Once cast, a vote cannot be changed. Methuselahs can gain votes in the following ways:
Political Action Cards. Each Methuselah may gain one vote by using a political action card.

(Emphasis mine, obviously)

Can a Methuselah burn a vote card during a referendum but not use the vote (i.e. abstaining) just to cycle?

No, once you've burned a political action to gain a vote you cannot attempt to do so again. But IANPB so, I'd be happy to be overruled.

I think you would gain the vote for the discarded card. You could then use it to cast it for, against, or abstain.
The vote you gain would be from the Methuselah, therfore cannot be canceled by cards that cancel votes from vampires.

Amenophobis wrote:

I think you would gain the vote for the discarded card. You could then use it to cast it for, against, or abstain.
The vote you gain would be from the Methuselah, therfore cannot be canceled by cards that cancel votes from vampires.

Correct.
Rulebook 6.3.3 : Once gained, a vote need not be cast right away, if at all.

Thanks Pascal and Amenophobis! I forgot that bit about not being messed up by cards that mess with vampire's votes.