Never heard anyone say "not" to eat. Your body is going to need all the energy it can get to make it up that mountain.
Seriously. I was doing great on day hike this weekend, but had real trouble keeping my pace once I hit Trail Crest. I'm pretty sure I bonked when my body just ran out of energy. I had only had 400 calories all day long and had been burning them like a steam engine. When I got to trail crest I had a Cliff bar, but it was too little too late. My pace dropped off and I was sluggish in every step. Those last two miles at half the pace were harder than the first nine moving quickly.
My plan was to fuel with gels every hour or so on the way up, but now I see that wasn't nearly enough.
The moral of this story?
Eat more, not less!