After a false start or two, I devised and executed a divide-and-conquer scheme and isolated the parasitic drain in around 30 minutes.
The original symptom was that the current draw never dropped below 120 mA (0.12 Amp). Testing was done by disconnecting the negative battery terminal and connecting a multimeter (on the 10 amp scale) between the negative battery terminal and battery cable and waiting 10 minutes. Waiting additional time never reduced the current further.
I started by exposing that fuse panel that sits atop the battery, taking off the fender brace and removing the cover. Inside are several high-amperage fuses ranging from 60 to 175 amps. A couple of these are bolted down including the ones to the starter and alternator. Three simply plug in using high-amperage connectors.
My plan was to see which one of these cable had the drain and use the schematics in the upfitter manual to see where the draining cable went. I first unplugged all three cables. Reconnecting the ammeter and waiting 10 minutes showed drastically reduced current draw, below 0.01 Amp.
Of the three cables, one has a single plug and the other two share a two-contact plug. I first disconnected the ammeter, plugged in the single cable (because it was easiest), reconnected the ammeter and waited. Current was still below 0.01 Amp.
Now I had to distinguish which of the two cables had the draw. The peak current when the ammeter was connected was around 5 Amp for a few seconds, then rapidly dropped to 1 amp. This was low enough that I could use a clip lead between one of the cables and the fuse panel. This caused just the other contact to still be isolated. Reconnecting the ammeter and waiting showed that current was back up to the high value of 0.12 Amp.
I wanted to make sure that the drain was actually on this cable. It could have been caused by a small current on this cable enabling some relay or computer that was draining current somewhere else. So I disconnected the ammeter (that allowed current to flow to the negative battery terminal), and then replaced the clip lead with a second ammeter, then reconnected the first ammeter and waited. Sure enough, the 120 mA was flowing through this cable.
Several minutes study of the upfitter manual showed that the cable in question powered only the fuse panel at the right end of the instrument panel.
Time to start popping fuses and checking the ammeters, one fuse at a time. I thought this would be tedious, but the second fuse I pulled dropped the current back to the low value of 0.01 A.
Back to the upfitter manual again. That fuse, F7DR, powers a signal that goes through a relay in the Body Control Module (BCM) and powers one low-beam headlight and a parking light on the other side. These were passive loads, on the far side of the BCM. Those loads couldn't have been responsible for the relatively small leakage. The problem HAD to have been in the BCM. I replaced the BCM and sure enough, the current dropped to the low value of 0.01 A.
That fixed everything but the nightmare problem of getting the vehicle to accept the new BCM. That will be the subject of another post.