when I first hit this site there were 2 tables that somehow disappeared but basically under title 10 the president directs you where you will serve. Under title 32 the governor can activate you but only in your state. Also

Natural disasters, such as Hurricane Sandy, raise questions concerning the President’s legal
authority to send active duty military forces into a disaster area and the permissible functions the
military can perform to protect life and property and maintain order. The Stafford Act authorizes
the use of the military for disaster relief operations at the request of the state governor, but it does
not authorize the use of the military to perform law enforcement functions, which is ordinarily
prohibited by the Posse Comitatus Act. However, the President may invoke other authorities to
use federal troops to aid in the execution of the law, including the Insurrection Act. This report
summarizes the possible constitutional and statutory authorities and constraints relevant to the use
of armed forces, including National Guard units in federal service, to provide assistance to states
when a natural disaster impedes the operation of state and local police.

Unless the President authorizes Posse Comitatus applies:
https://fas.org/sgp/crs/natsec/RS22266.pdf

The Polack MSgt

(13,478 posts)

4. A governor has limited authority to mobilize National Guard troops

Reply to Trueblue Texan (Reply #1)

Wed Jun 30, 2021, 07:19 PM

Jun 2021

Without approval from the President. That authority is one of the main benefits a State gets from a Declaration of Emergency...

So the article explains the 2 ways National Guard units are authorized to activate and conduct missions.

They can't be activated and sent on a "Mission" outside of their home state without legal authority.

Each of the Soldiers and Airmen serving in the Guard is entitled to pay and benefits - including accruing Time in Service/Time in Grade point when they are activated. Survivor benefits in case the worst comes to pass. Access to VA care if needed.

Without the Commander in Chief's authorization they are not allowed to operate as an official unit except for a limited time on the Governor's orders in state and paid for with State money.

A governor can't just use the Guard as a personal task force and get a billionaire to foot the bill.