That is it and the price sounds right to what I paid.
Others can speak more "mechanically correct" than I can, but the way I see this solenoid operating is that when you turn your key switch to the "on" position, it closes and provides power to the bus bars in the electrical compartment. Many 12VDC items work off those bus bars, including your starting circuit. First indicator I had problems was I had NO red warning/"idiot" lights on the dash panel as I would normally have when turning the key on. My first attempt to fix this problem was replace the key switch. That did not work. I would not be able to start the coach until I got those lights to come on. I would sit there and turn the key off and on multiple times until finally those lights would come on. And then I could turn the key to the start position and the coach would fire right up. But beware! If this is what is happening to you, then replace that solenoid! Because one day you will be going down the road and that solenoid will drop out and your coach will go dead. I was lucky enough to be able to start it while still rolling down the road. Once I got home, I went searching for the problem again and found information on this site about this solenoid. I replaced it and everything worked fine again. About a 1-1/2 years later I had the same problem again. Those solenoids don't seem to hold up well. I replaced it again and put a spare one in the Barth. And now I also carry a spare in Barth II, just in case. Some of the problem may be that things get added to the coach and the load on those solenoids gets to be more than they were originally designed for, therefore wearing out the solenoid faster than normal. I tried to find a replacement with more current carrying capacity, but to no avail.
My experiences with these type of solenoids goes back to my earlier years and my Fords. I should have remembered those trials and tribulations, as I used to carry a spare solenoid with me back then because those would go bad on a regular basis. And it always seemed to go bad when I needed the car the most...

I did install a new solenoid as advised today and engine did start, and more surprisingly no extra parts! Obviously with an intermittent problem, I can not be certain this is fix but time will tell.

I am currently struggling with this same concern and have tracked it to the allison transmission controller. The wire that kicks the starter goes in and out of the relay box.

Problem solved with the placement of a jumper between the two previously mentioned wires.....Only time will tell.

Crawl under the coach and look at the starter solenoid. There is one 12v wire from the ignition to the starter solenoid. That 12ga wire will develop corrosion in the crimp connector that is the ring terminal to the solenoid. You can use a vampire crimp connector to add another 12ga wire from just about anywhere along the wire that is above or in front of the exposed portion of the wire to the terminal on the solenoid. Chances are that will fix the problem. It did on mine.

With one person holding the key in the start position, get under there quickly with a volt meter and check for battery voltage on the "S" terminal of the solenoid. If B+ is present, check for B+ at the large terminal on the lower part of the solenoid sending B+ into the starter motor. If you have B+ at both locations then you have an open inside the motor, perhaps an open commutator bar. The starter has to stop on the faulty bar to fail. If you DO NOT have B+ at the large terminal then the contacts within the starter solenoid have carboned up creating excessive resistance. In either case, whack the starter with a hammer, if the engine cranks up, you can get to your next destination. You can purchase a replacement solenoid if needed. I do not believe in changing parts without proving that they have failed. Good Luck!

I just read the thread on the solenoid that is in the drivers door area that everyone was saying had a high failure rate and it occurred to me that the wrong solenoid is be used. The E85 solenoid is an intermittent use solenoid not a constant duty solenoid and based on the description of how it is used it must be a constant duty to survive.

The Echlin ECH ST 85 Solenoid relay that is mentioned IS continuous duty and so specified in the Echlin catalog

HTH