There is a formal process for pardons that is fairly lengthy. What usually happens is that someone contacts the Department of Justice and applies for a pardon. This application is then reviewed, and the DOJ makes a recommendation to the President regarding the pardon.
While this is a fairly lengthy process, it is only followed by convention, and is not necessary for a pardon to occur. The Constitution gives the President the power to pardon, but does not give any requirements or procedures that must be followed.
Trump pardoned Sheriff Arpaio in 2017, and did not follow the above procedure at all to do so. There was a document that was signed, so presumably if the document was prepared in advance, the pardon could be executed as quickly as the President could sign it.
Could the President scribble out an order to pardon on the back of a napkin and sign it while sitting through the impeachment vote? I am definitely not a legal expert, but given that the Constitution does not have any procedural requirements whatsoever, I don’t see why a scribble on the back of a napkin wouldn’t count.
Would a tweet count? Probably not, given that a tweet could easily come from a staffer and you would have a hard time proving that it actually came from the President.