My guess is that there's NO fuel in the rear bowl.
What type of bowl? (Dual inlet or fuel transfer tube?)
Are there no sight plugs on that bowl?
Needle / seat stuck?
What is the Holly List Number stamped on the front of the choke housing?
It would be much easier if we could identify the carb and/or have some pics of it.
You mentioned doing a carb overhaul ... I'm assuming this carb to be a 4160 series with a metering PLATE, not a metering BLOCK with removable jets, right?
If so, I seem to recall that most kits include metering plate gaskets for both 4160 (square bore) and 4165 (spreadbore) carbs. Any chance that you may have installed the wrong gasket and blocked the hole in the metering plate? (Just a thought ...)
Holley #108-13-2 Fits 4160 Chrysler
Holley # 108-27-2 Fits most 4160 models