Voting for a third party for President tells them running in a fake Presidential election can get your vote, and with your vote likely comes some of your time and attention, despite the fact that the election is fake since most people just pretend all votes are counted while several states don't count them.

Voting down ballot while writing in nonsense for the Presidential part of the ballot, or leaving it blank, sends the signal that you aren't pretending to recognize the federal government and your interest in local politics is only focused on resistance.