If a light works when it's the only light turned on; but stops working, or goes dim, when a second light is turned on, it is usually the ground, usually a dirty/poor ground.
However, it may not be the ground wire, it may be whatever the ground connects to.
For example, a taillight may ground onto the bed, that connection may be good and clean; but the bed needs to be well grounded for the lights to work.
The same applies to the front fenders, they need to be well grounded.
Yes, a light assembly shares the ground with all of the lights in the assembly, a poor ground will effect all lights in the assembly.
A good way to test is to connect a test wire to the battery ground post and touch it to the ground at the light assembly, if the lights work as they should, the problem is between the light assembly and the battery
However, it may not be the ground wire, it may be whatever the ground connects to.
For example, a taillight may ground onto the bed, that connection may be good and clean; but the bed needs to be well grounded for the lights to work.
The same applies to the front fenders, they need to be well grounded.
Yes, a light assembly shares the ground with all of the lights in the assembly, a poor ground will effect all lights in the assembly.
A good way to test is to connect a test wire to the battery ground post and touch it to the ground at the light assembly, if the lights work as they should, the problem is between the light assembly and the battery