Asked to write a letter of recommendation for promotion for an abusive former professor
Get your former advisor to sign the letter now.

After that has succeeded or failed, you should contact the person who runs this process and ask them verbally how the letter will be used and what it contains.  Probably this is a dean.  Probably the dean already knows about your advisor's behavior.  They might be seeking a letter that will help them get rid of your former advisor.  At well-run universities, these letters are not requested from random students.  They come from known students.

You should write an honest letter.

There is an option you do not mention:  You can "damn with faint praise."  This is done by writing a letter which says nice things about a person, but none of the nice things are relevant to the person's job.  E.g. They are funny and well-dressed.  I don't recommend this but it is available to you.  If done carefully, it can prevent promotion while giving the illusion that you intended to help the advisor.