If he really wanted to keep out illegal immigrants he'd do what Japan or China do. Require verification of legal residence from everyone for job, schools, etc. No fences/walls needed.

Or he could ask someone to develop an app where people could report people who are working without proper docs and fine the workplace and schools for violations. It could even be incentivized and non false positives get rewards of some sort --tax credit, whatever. False positives get demerits, etc.

That said, if employers are not willing to pay citizens a minimum wage of $15, then we will need a way to allow cheap unskilled imported labor to work on farms etc. Set up a system where you allow seasonal work visas. If you overstay, you are out 5 years. If you want to stay past a season extend your visa by exposing someone overstaying their visa so you get self policing. However, since this creates underemployed citizens, tax the employers who employ imported labor to underwrite citizen unemployment benefits.