The way I understand the rest stop / gas delivery is this:
Bryce called for gas at 9:00 am from Buttonwillow, it was delivered sometime after but we don't know exactly when. Around noon his mother received a text survey asking about the service call, and this was the first indication she had that Bryce was not in his apartment in Rocklin.
She most likely called him but he didn't answer, so she called the service company, talked to the delivery person (Christian) and got him to go back and check on Bryce around 12:30, which would have been 2-3 hours after Christian delivered the gas.
I remember reading that one of the 2 times Christian went to Bryce's car, Bryce was not IN the car, and "may have been sleeping" according to Christian.
Bryce's mother did not speak to Bryce until that evening, when after he still hadn't arrived, she called the police, and they found him on Lagoon Drive in Buttonwillow at 9:00 pm. They probably also told him to answer his mother's calls from now on! Which he seems to have done a couple of times.
I have no idea why he would have stopped the car in the Buttonwillow area other than running out of gas, but as for what he may have been doing there if he wasn't sleeping - could he have been playing video games on his laptop? Could he have found power to recharge the laptop at the rest stop? Would he have needed wifi? Maybe that's why he moved to the location near the motels?
I'm pretty sure my son could spend 9 hours playing a video game, losing track of time,and being irritated at any interruption like Mom's phone calls, gas delivery or police check. JMO