First of all, there was most likely no wiring done by a dealership Tech and you more than likely have an open circuit that's causing the problem. The previous owner also most likely thought telling you he had this done in order for you not to think there was a problem with the '05 Escape. The problem could be any number of things and you need a good Tech to trace it down with pin point test and his diagnostic tools.
If I was the Tech you brought your problem too and told him an unapproved rewiring job was done, I'd tell you you may have big problems. The headlights are controlled by the multifunction switch and the Smart Junction Box (SJB) that controls many other functions. Someone attempting to rewire around a system that is programmed does not know what their doing. The Tech can follow procedures to program Daylight Running Lights (DRL) on or off, but he can't or shouldn't try to reprogram the SJB to keep the headlights and taillights on when the key is in the run position. An example, your SJB may need replacing and all the new SJB are programmed without DRL. Your laws require DRL so the tech replacing the SJB should reprogram DRL in the new SJB. No rewiring is done!
The fact that your rear washer pump causes the lights to go out is strange, but we're dealing with programming in the SJB that has a conflict with both those systems working at the same time. You could have an open circuit, bad switch or even a bad SJB. I suggest taking it to a dealership to diagnose the problem and call you with an estimate to repair. Either that or get yourself a battery operated portable radio for camping. | 
