I think the Daytime Running Lights run on AC current. Well, if not AC, then pulsed rather than DC. If that is the case, you may be getting feedback from the DRL to the rest of the electrical system.
I would attempt to turn off the DRL system, or remove it from the circuit, to see if the pulsation stopped. If it did, I would expect that there is a feedback from the DRL to the rest of the system. When you turn the headlights on, the DRL is disabled, which would remove the pulse, as you report.
tom
Edit: The DRL is not run from A/C current, as I just looked at a PDF of the 2001 escape headlight wiring. If you pull the DRL relay, the lights will not come on unless you manually energize them. I think that will disable High beams...
That would be a good test, but I am thinking that you have an A/C ripple in your alternator output, which can only be 'seen' by an oscilloscope. You may be able to detect A/C with a DVOM.