On my return to LAX, I saw this Southwest plane parked at T2:
I asked a ticketing agent about the shuttle service. Apparently, the service starts June 4 to allow for connecting pax to fly to Liberia, Costa Rica. My seatmate on LAX-LAS came off that flight. The shuttle service will run between t1&t2 airside every few minutes. WN will also open a dedicated checkin counter at T2 in June for their international flight to allow for departures to occur from T2 instead of the current arrangement where the flight arrives T2 and departs T1.