Manpower is infallible. The more people you have patrolling, the more chance that they will discover tunnels wherever they exist. As for overstaying the visas, that's a CIS issue, and has nothing to do with the construction of the wall. That could use its own funds too.
The key is to fund things intelligently and not go above and beyond to secure extra measures when what you have is already enough. It's like if they raised the police budget 50 million dollars so they could plate their cars in gold foil and look cooler. That's not going to do anything, but if you used that 50 million budget to employ more police and have them patrol longer, then you actually make good use of that money.
It looks like you keep implying that the wall will be the only thing going into border security and that border walls are useless blah blah blah
It's a good idea to bring up Israel in a conversation like this

They have an extremely effective wall even though it kinda looks like a bunch of spray painted dominoes and toilet paper rolls. And that's on a border
with a terrorist state that calls for the death of Israel and Jews globally. All we have is a failed government that barely controls it's own land and is trying to beat out it's southern neighbors in the "how fast do you need foreign aid" race. And Israel is basically a giant desert with a few big cities which is a pretty good comparison to the southern border. There's no reason why a country ten times as powerful and with a tenth of the problem can't handle something like this. And are we really supposed to give up all hope on a wall because some people will try to dig under it? Is that it?
That's like saying if a gun shoots dead straight four times out of five we should give up because it doesn't shoot straight once?