Update: I have run ground wires (old extension cord, thanks to a tip I read on here) from where the negative battery cable attaches to the frame back to each of tail lights. I now have 0.1 ohms between the negative post of the battery and the ground wire at the tail light.
But the lights were still way too dim. Starting at the positive battery I have cleaned or made new connections all the way back to the tail lights.
Here are my voltage readings now with the headlights on:
Battery: 6.1 volts
Battery cable connection to starter: 6.0 volts
Ammeter: 5.9 volts
Connection at light switch from ammeter: 5.8 volts
Fuse box in: 5.6 volts
Fuse box out: 5.6 volts
Junction at back of truck where tail light wire splits off to both tail lights: 5.2 volts.
So it looks to me like that last reading is excessively low. When I separate the wires at that junction, the voltage of the wire coming from the front is 5.6 volts. If I add the wire going to the left LED tail light, it is still 5.6 volts. But as soon as I add the wire to the other tail light, the voltage drops to 5.2 volts.
Is that normal? The other tail light is still my old one with bulbs, and I haven't checked the connections from that junction to it yet. I am using a wire nut to make the connection at that junction. Is that a no-no? I like being able to take it apart.