Well...I'm not sure BL had the knowledge to get his van into Mexico. Getting over on foot is fairly easy (although most people wouldn't know how to do it). If he searched how to get his van into Mexico from his or Gabby's phone, LE would know that. I guess he could go to a public library, but apparently he drove straight home (which tells us something about his psychology and mental state).
He would be seen at a border crossing. Without applying for a permit (which is supposed to be visible on the window of the vehicle), one cannot go more than 20 km into Mexico.
At any rate, his DL and his car's license plate would both be recorded and readily available to LE. To get that permit to travel further into MX, it's my understanding you
do need a passport.
Crossing the U.S. - Mexico Border by Land
And there's one more tricky detail for him - since he would not have the permit, they'd run those license plates and the person to whom it is registered would not be in the car. He'd be directed to a special lane, held up for hours, while the actual owner was located and his story checked out (friend allowed him to borrow the car). What one does is get a notarized letter saying that you have permission to take that car into MX and even then, you'll be sitting there while authorities check your ID against US databases.
Now, having said that, people steal those permits from cars and use them to steal cars in the US and get them deeper into MX. Or they know back roads (especially out of W. Texas, NM and AZ - less populated areas). If he looked Mexican and spoke fluid Spanish, he might have had a chance on back roads. Otherwise, the people who do control those back roads would be very unhappy to see him and assume he had stolen the van.
His best bet of getting into Mexico is to use one of the numerous illegal crossing points - by foot.