I tried that approach some years back, when I had a bright green Datsun 240Z (a beautiful '72, actually...the very best year for the venerable 'Z-car').
One day I was driving along on the freeway's middle lane locally and at the speed limit, and had to get into the right hand lane to prepare for an upcoming right-hand turn off the route. Looking behind me, I saw the path was clear (no cars within a 150 yards or so), turned on the turn indicators and began a right-side merge with that lane. All well and good, but meanwhile, some fool in a new BMW came fast-lane-switching through the traffic and was right on my tail in a heartbeat. Apparently the fact that there was now someone blocking his impatient progress infuriated him and he swerved out on my left side and began to scream epithets at me. Whaaaa?!
I was in a good mood and decided that, despite his being a total as*hole, I'd let it slide and did exactly as our cabbie friend suggested: grinned broadly and gave him a shaka (Hawai'ian 'peace' sign).
Mu unwillingness to be drawn into his hissyfit, instead of defusing the situation, seemed to send him over the top and he began driving dangerously...cutting me off, pulling ahead of me and slamming on his brakes, etc., etc., etc.
This to me a classic instance of how no matter how hard one tries to me 'nice' and sluff off irrational angst-dumping by others, nothing is going to avert a potentially serious crisis if the other individual has become so irrationally bent on a 'crash' as this chap obviously was. It could have quickly escalated into a gun-flashing, full-on road-rage encounter, had there not (fortuitously) been a CHP car coming up on the scene quickly from behind. The miscreant then decided not to further exacerbate the encounter and pulled away. My turn-off accomplished, I later mulled the whole incident over, realising that ultimately...and depending upon the mind-set of the aggressor...there's NO universal antidote to this sort of thing, these days.
Afterwards, I returned home, pulled out a volume of Robinson Jeffers poems from the shelf, grabbed an H.L. Mencken work and silently reaffirmed my sympathy for Jeffers' misanthropic social outlook ('Love individuals, hate humanity as a whole'). [More of Pogo Possum's famed dictim, "We have met the enemy and he is us..."]