I could not remember, so I just now checked my own car
HEI modules should NOT draw current through the coil with key on/ engine off.
I 'spose maybe some offbrand units do.
Make SURE the module is grounded
Turn key on/ engine off and check both sides of the coil. You should read "close to battery" on both sides of the coil, as well as the battery feed terminal at the HEI
Could be your dist. The current in the pickup coil is VERY low, and those connectors do become corroded. Wiggle the dist. connector in/ out to scrub the terminals clean, and "feel" how tight they are.
Put your meter on low AC volts, hook it to the two disconnected distributor pickup coil terminals and crank the engine. The dist. should generate nearly 1V AC
A SIDE NOTE. your reading of 11.X volts is LOW. This may NOT have any bearing on the problem, but do the following:
First, check for voltage drop in the ignition harness, which will ALSO cause overcharging. To do that, turn the key to "run" / engine off. Hook one probe to the positive battery post, and the other to your ballast jumper. You are hoping for a VERY low reading, the lower the better. If over .2V (two TENTHS of a volt) try to find out why, and if it's more tha .3V or more, get more serious.
You are checking the circuit path from the battery -- fuse link -- bulkhead connector -- ammeter circuit -- ignition switch connector -- through the switch -- back OUT the switch connector on the DARK BLUE ign "run" wire -- back out the bulkhead connector -- to your ballast jumper.
ALSO check your resistor bypass circuit, which is NEEDED for starting. To do that, hook your meter to the ballast jumper and ground. Crank the engine USING THE KEY. DO NOT jumper the start relay for this test. You should read "close to battery" during cranking, and at LEAST 10.5V
If all the above checks out, try to check the coil TO DO THAT, obtain 'any' distributor points condenser (capacitor) or even use the radio suppression condenser, which should already be on the coil. FOR THIS TEST ONLY move the condenser from the coil NEG to ground. "Rig" the coil up with a high tension test gap, such as a plug wire and spark plug. Just lay the dist. on the fender, or even leave it installed.
Now, take a clip lead and hook the coil POSITIVE terminal to the battery.
Take a second clip lead and hook it to the coil NEGATIVE post. Take an insulated screwdriver, etc in the end of the clip lead, and every time you short the coil NEG to ground AND THEN remove it from ground, the coil should make a spark.
If this checks OK, replace the HEI module. You really should have a spare anyhow. Buy a good quality one like a Blue Streak