Flickering or pulstating Headlights

OK. If that mades sense. Then lets illustrate the flow path in relation to voltage.
Orange dashes represent current flowing. Arrows indicate direction by common convention. (ie Current flows from higher voltage to lower voltage).
Engine OFF, Key in RUN.
View attachment 1715324487

If there are no shorts, just a few amps are flowing.
If all connections and wires are in perfect condition voltage at the bulkheads, Alternator B stud, Resistor J, Alternator F+ will also be 12.5 Volts.
Voltage on the other side of the resistor will be less the 12.5 Volts. Voltage at F- may be close to zero.

Since you measured a 1.5 Volt drop at the regulator, connections or wire along that path has resistance.
There was also a voltage drop when the engine was running.
Not sure what the voltages were at the VR and alternator, but the instrument panel meter is probably connected downstream of the fusebox run/accessory side.
If so, then the flow path that overlaps in both situations is key Run connection to the regulator sense terminal.

But there could be more than one poor connection or wire. Therefore check for voltage drops under load.
Here's another example. Its wiring is the same as previous example (doesn't show you've installed a relay for the ignition and field.)

Engine Running. Lights On, Heater Fan on Low, battery recharged.
View attachment 1715324492

If all the connections and wires are good, voltage at alternator B stud, the bulkheads, and the battery positive terminal will be the same.
Illustrated above is:
1 amp to the Mallory CD box
9 amps to the headlights
5 amps to the instrument and parking lights
3 amps shown going to the heater fan (low speed)
2 amps to alternator field, 1/2 amp or less to Mallory on switch.

Thank you for the images that really helps me understand what's going on. I'll test the voltages at the places you mentioned when I have some free time over the next couple days and report back.