Our home has a brick chimney with two flues for two wood burning fireplaces that are no longer used. I keep the lower dampers shut but was thinking of covering the top outlets to prevent cold air/pests from entering the chimney. Eventually, the fireplaces will be covered with insulation/drywall/etc.

My chimney looks similar to this and is on an exterior wall:
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Based on this article from Fine Home Building, I was just going to place a 2x8x16 stone patio paver over each outlet and call it good. They also mention a chimney balloon but I don't think I will bother with that.
But upon further research, I see some people claiming that the unused chimney still needs ventilation and that air bricks should be installed to prevent condensation?