Never. Don't even bother trying to book for an EUA (I have only heard about these mythical EWR-SFO EUAs on Sat. mornings from friends). I fly EWR-SFO and back 1-2x per month and I am 0 for 50-something and counting as a Plat, which includes H-fares. I have flown mornings, afternoons, evenings on every possible day of the week.
If you want an upgrade, fly to SJC. You are limited to 1 direct flight each day from EWR, but if the times work, you have a good shot for an upgrade as a Plat.
On a positive note, I flew back from JAX today in the front of the plane on an EUA, making me 2/3 this year on non-EWR-SFO/LAX flights...what a nice change from seat 14C. LOL