I would make a backing track and put the guitar down and then get a vocal mike and just sing. I wouldn’t use any lyrics, but just sort of hum melodies that I may want to use. The reason I put the guitar down is because I didn’t want be influenced by my guitar vocabulary. I didn’t want to play the licks that I normally know or gravitate toward because I know them. So write by humming, to me is a very natural way of writing. And after I have something I like, I record it, get the guitar back up and copy what I just sang.
Actually, I’ve been using this method for years and this is in fact the main technique advocated by Jason Blume in “6 Steps to songwriting success”. According to Blumes the vocal melody is the most important part of the song as it is the one people will remember, even when they don’t recognize the words or the chords. So humming a hook is one way to make it more memorable. Plus, it doesn’t require any knowledge of an instrument.
What’s most fascinating is that Gilbert does this to keep his guitar wizardry from influencing the quality of his songwriting. That’s something only a great songwriter can recognize.