It is my understanding that the IRS allows the SSN of the grantor to be used as long as the grantor is living. If the grantor is no longer the trustee, can the new trustee sign the W-9 certifying the SSN for the trust? Would this be one of the authorized actions of the trustee? The grantor may be incapable of signing?

As I recall, the grantor and trustee must be the same person to use the SSN of the grantor for the trust. If the grantor is no longer serving as the trustee, I believe an EIN is required.

The IRC lists several characteristics that might make a trust a "grantor" trust. One is if the trust is revocable. Another is if the grantor is the trustee. There are more.

Generally, a grantor trust does not need an EIN until it becomes irrevocable, i.e. after it stops being a grantor trust. That is usually upon the death of a grantor.

A trustee could certify an EIN. Only the grantor or someone holding a POA giving the attorney-in-fact sway over income tax matters could certify an SSN.