The turn and emergency signals are a relatively slow frequency square wave, and this is where an old analog meter is superior to indicating what is going on. It is the sampling rate and update time on your digital meter that is not telling you what is really going on.
You will see at each bulb two wires - the black wires are the ground (57). Do the wires jumper from bulb to bulb? From the outboard bulb, does it then, like the Mustang, tie into the circuit that includes the backup lamp?
If you can install a jumper, like I recommended, from the ground screw that you cleaned up, to the bulb socket that can help you determine if there is a poor ground between the lights and the ground screw. From the looks of it, that might be difficult. I would probably pull the inboard most lamp, pull the bulb, and probe the ground pin, with an alligator clip connected to the ground screw, and then see how bright the lights are.
The other option is to pull all of the bulbs and connectors, and give them a good cleaning.