TSA orders airport valets to search parked cars

It counts as a government search as it is being done at the direct behest and under the authority of a law enforcement agency. This is old case law and is pretty well settled at all levels. (I am not a lawyer but did work for 25 years in Intelligence). A cop cannot order a citizen to go search something just to evade Constitutional or legal restrictions.

if they simply asked attendants to note anything suspicious and report it, they’d be on a lot firmer grounds but ordering someone to carry out a search for you essentially deputizes them fo that purpose.