Also if you aren't in a sleeper on either the Lake Shore or the Builder, you can buy access to the Metropolitan Lounge there for $35(?). They always have Red Caps for Builder boarding there, they'll announce that passengers needing Red Caps to meet them by the entrance desk, those not needing Red Caps meet at "back door" by the restrooms/showers to be escorted to the platform (aka kindergarten walk).
I don't know about the wait for Red Caps on incoming trains. I don't typically use Red Caps except at NYP when I'm not in sleepers to get a jump on the crowd.