Other people have suggested similar things, but I’ll take it a step farther: the issue may simply be fidelity of sensory input neurons, i.e. different things count as “having taste” for different people. I assure you, you could give me olive oil so lite that it glowed, and it would still have a very distinctive and strong taste to me.
This, I guess, is where the noseclip suggestion came from.
I have an (I think) better idea: “drink” the stuff by putting it in a (clean!) turkey baster, stick the turkey baster in the back of your throat, and squeeze. If you have a gag reflex problem, not so much, of course, but I’d sure be interested to find out how that works for people who have tried the diet and had it fail.
When extra light olive oil didn’t work, I tried taking oil in the form of swallowed flax oil caplets. Swallowing twenty of those wasn’t much fun, but it still didn’t work.