Voltage Regulator?

The 1.1 is likely the important reading. You must measure with everything connected normal, because current through the circuits is what causes the drop in the first place. You measured this 1.1V exactly where? At the VR IGN terminal to battery PLUS?

"Let's say" your VR is correctly operating at 14V nominal. That 1.1 gets added to, so the battery will "run" at 15.1

One way I've suggested curing this is to cut (electrically, several ways physically to do so) the dark blue "IGN1" "run" wire coming out of the bulkhead into the engine bay. Feed the bulkhead connector end to a relay coil, feed the relay contact from the starter relay with a large fuse or breaker, say, 20A, and connect the engine bay end of the cut wire to the relay switched // load contact

Now the VR and underhood loads will be fed directly from the starter relay, instead of "loading" through the "circuitous circuit" through the harness