I know some people do it and I love Geoff's channel, but maintaining a spread while vibrating with the 4th finger just doesn't compute with my brain or body.
I know that vibrato is different with pizz and arco, a phenomenon I plan to research explore in depth later because it fascinates me...how can the same vibrato in the left hand sound wider when plucked than while bowed? What is the science behind that?... so I'll limit my comments to pizz vibrato here because I am at such a rudimentary level with the bow that it would be disingenuous to claim otherwise.
But in the realm that I use vibrato, it is like every other left hand technique in the respect that I feel it does not require the thumb to occur; the thumb provides an anchor and allows a higher level of precision and control, but is not needed to provide the force.
I am not aware of an instructional video about playing as though every note might use vibrato WRT the left hand, but at the past few ISB conventions I have seen more and more players playing in a style that features a relaxed LH shape; for some, it seems to be a technique that alternates with the more traditional approach, and for others, it seems to be their primary bread and butter. The example that comes first and foremost to mind is Joel Quarrington, whose left hand caused 500watt lightbulbs to fire around my brain when I finally saw him play live. Further research into his concept largely confirmed what I had seen live, especially as regards his extensive use of playing on the pads and the angle that the strings track across the fingers. These largely mirror the concepts I had been exploring on my own in a different context (and obviously on a much less advanced level).
Here's a thread about his concept.
Here's a blurb from his book which explains more about the concept. I think this small bit of information falls under educational use:
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This all resonates with what my body is telling me.
Finally, here's a video where you can see some closeups of his left hand doing a lot of "relaxed hand shape" playing: