The Work Number, an Equifax service that a shockingly large number of employers provide data to. If your new employer is one of these, and it probably would be unless it's a startup or a small family business, your old employer can see that you're now employed and who with.

A lot of the high paying industries with non-competes are small and insular. If you violate your non-compete and are found out you will go to arbitration, probably get fired from your new job and have expensive legal fees (half the cost of arbitration + your lawyer). That's before the results of the arbitration.