I probably spent hundreds of hours on the phone with EB. He believed that "bigfoot invisibility" was the creatures natural ability to produce a "low-level hum" of sorts to place its viewer in a hypnotic state. He gathered this from Native American witnesses and Asian cultures.
In the same manner that "buddhist monks" place(d) themselves in a trance with this type of "hum"; and along the same lines a hypnotist would swing a pendulum and use a "certain tonality in his/her voice" to induce hypnosis - this is what EB believed. We spoke of it many, many times.
I believed he called it "infrasound". If the bigfoot had the ability to fool the mind of its on-lookers' in this fashion - I would not be surprised. Heck, at one time we modern humans might have had these abilities (before we became domesticated). Over time, we've clouded ourselves and lost these abilities due to our "personal involvements" with daily jobs, worry, stress, modern religion and the like.
So, can the bigfoot seemingly "disappear at will?" Maybe. Especially if it had the ability to control infrasound and produce desired results in its victim. It wouldn't really be "gone" so to speak - BUT your mind would think it had disappeared. This is nothing "magical" (its biological and physiological). Infrasound is a very real thing that could have adverse effects on emotion(creating a fight-or-flight syndrome), sight(disturbing optical responses) or beliefs(anyone not familiar with infrasound may take it as "something magical").