I'm no special expert on options and their Greeks. However, I have had a decade plus experience of almost-daily discussions with a bank derivatives desk, on pin risk and the behaviour of autocallable, cliquet etc. structures.
You are correct that a gamma hedge would require an options as opposed to underlying hedge. However, the traders' obsession with gamma didn't (to me) seem grounded in any obvious desire to gamma-hedge. It was more focused on the effects of gamma on delta, if/when the price moved. Because that would have differing effects on the behaviour of delta-hedgers. Either a positive feedback loop, where price moves would require increasing intervention in the underlying; or negative feedback loops, where price moves would generate offsetting hedging, pinning the price. As such, the real effect of the gamma positions run by delta-hedgers was seen more as a driver of future realised volatilitym and thus relevant to the desk's positioning in VIX/Vstoxx product.
Even when there was perceived to be some "cliff" where the market dynamics given any change in price might shift, it always seemed implicit that the hedge remained the underlying index futures. They just needed to be traded differently in that scenario, Or so it seem to semi-educated laymen like me ;-)