Have all illegals that are caught sentenced to work on the border fence for three years. When their time is up send them home.
Illegals can make compressed earth blocks (CEB) which are a way of turning mud, clay and sand into blocks that can be used to build the wall. They can also build the wall under supervision of the Army Corps of Engineers.
Make the base of the wall 12 or 15 feet high and wide enough to put a vehicle path on top. Every mile or so, put ramps on the inside so a vehicle can drive up to the top. On the Mexican side of this road at the top of the wall, put an additional fence 10 feet tall, topped with concertina wire.
Also use the blocks to create posts or barracks for the border patrol and connect theses posts via a train that provides connections and resupply. The train line can also be used to move the CEBs and other construction materials and equipment from the interior out to the construction site to build the wall.
Reorganize the Border Patrol into the Border Guard, similar to the Coast Guard, and train them as both Infantry and MPs. Illegals caught by the Border Guard should should be fast tracked via a separate court system that determines if the individual is an American citizen and if not, then is sent back to the other side right away.
The e-verify system should be integrated between SSN and IRS data to identify those SSNs that are reporting incomes 1) from different addresses 2) from dead people, flag those accounts as requiring additional verification.
ICE should be re-tasked to the IRS for the purpose identifying those businesses that are using illegals and charging those businesses with tax violations. Businesses that use illegal aliens should be restricted from declaring dividends for the year in which they have hired illegals and taxed at 40%. Use of e-verify would be protection against this action.