Who puts TIN on HUD-1 when Trust is seller?

When signing the HUD-1, I’m assuming only the trustee does that but then it also has spot for TIN (Tax ID Number) for the seller. If the trust is the seller what do you put there?

Does the trustee put their SSN or do you put the beneficiary’s EIN number if beneficiary is LLC?

Does the TIN need to be filled out on HUD?

I am pretty sure that a trust does not need a tax id # due to the fact that its reported on the owners 1040