I didn't mention that I have always sealed those screw connections with Vaseline and in the last few years I also spray with Rust Check film. I then thoroughly wrap the whole back end of the plug and the cable with electrical tape. On the big trucks I also covered that with brush-on electrical tape or brush-on contact cement (same stuff at half the price). Fluid film should work.
This has given me an idea. First, I'll try getting just the plug replacement. I'll spray the contact points with something like Battery Saver. I'll then tape over the seam where the wire enters the plug. Over this I'll brush on some of that rubberized tool handle dip and see if it adheres to the tape and plug base. If it works, it may provide a decent weather seal. Thanks to all who contributed in a fruitful manner. It seems when people here do that, one idea leads to another to hopefully solve the problem.