Here is the Texas statute. It does not specifically require the operator, if the registered permit holder, leave the vehicle while parked in the space.

Sec. 681.006. PARKING PRIVILEGES: PERSONS WITH DISABILITIES. (a) Subject to Section 681.009(e), a vehicle may be parked for an unlimited period in a parking space or area that is designated specifically for persons with physical disabilities if:

(1) the vehicle is being operated by or for the transportation of a person with a disability; and

(2) there are:

(A) displayed on the vehicle special license plates issued under Section 504.201; or

(B) placed on the rearview mirror of the vehicle's front windshield a disabled parking placard.

(b) The owner of a vehicle is exempt from the payment of a fee or penalty imposed by a governmental unit for parking at a meter if:

(1) the vehicle is being operated by or for the transportation of a person with a disability; and

(2) there are:

(A) displayed on the vehicle special license plates issued under Section 504.201; or

(B) placed on the rearview mirror of the vehicle's front windshield a disabled parking placard.

(c) The exemption provided by Subsection (b) or (e) does not apply to a fee or penalty:

(1) imposed by a branch of the United States government; or

(2) imposed by a governmental unit for parking at a meter, in a parking garage or lot, or in a space located within the boundaries of a municipal airport.

(d) This section does not permit a vehicle to be parked at a time when or a place where parking is prohibited.

(e) A governmental unit may provide by ordinance or order that the exemption provided by Subsection (b) also applies to payment of a fee or penalty imposed by the governmental unit for parking in a parking garage or lot or in a space with a limitation on the length of time for parking.