Just to make this a duet, the reference to "estate" is a reference to property, not death. Ray's right, a financial guardian is as responsible for an "estate" just as a personal represenative is responsible for an "estate."
In an effort to maximize the IRS' chances of hitting the appropriate name/TIN combination, I suggest you use "John Brown Estate, Jane Blue, Personal Representative." (Put the name at the beginning of the account.) It's the fiduciary title that is your clue to the situation and the correct TIN.
And the last chorus: A decdent's estate has an EIN. A guardianship estate should use the SSN of the person under the disability.