I had to replace my solenoid a couple years ago. Different kinds though, not sure if mine is the same as yours or not. attached is a pic of my old one....jumper cables attached to the terminal so hard to see the whole thing, but only photo I have.
not sure, but I think this is the one I replaced it with (didn't pay that price though!)
https://www.aircraftspruce.com/catal...oidx610028.php
I discovered mine was bad while boondocking at sun n fun aviation convention/fly-in. My house battery was dead in the am after very little use...it should have been fully charged after a few ours drive to get there the day prior....so I did a little troubleshooting.... and lucky that at sun n fun, there are lots of vendors selling parts of all kinds. I was able to walk to the show and quickly find a continuous duty solenoid...and even though it was "aviation" grade it was inexpensive...and an easy swap.
Mine was rusty too, by the way. I coated mine with some of that red battery terminal spray in an effort to protect it. Reminds me I haven't looked at it in a while!
Good luck with yours!