Thank you all so much. I think this is a glow plug issue.
Secondly, I apologize. The WSM I have is a print out that was stuck in a binder with a bunch of pages out of order (that's how it was shipped to me). I sat down today and properly reorganized it. I had been struggling to find detailed troubleshooting because I had been looking in the 9-M section, not the 9-S section.
In the 9-S section, and in the copies white tiger so kindly included, it shows the glow plugs are supposed to read, factory spec, 0.5 ohms. Mine are reading 1.6 ohms. That leads me to think the glow plugs are burned out.
Now, I am going to do a little more double checking before I order glow plugs, but I expect that is either the main issue, or a big part of it. There may be a secondary issue, more on that below.
Thirdly, I apologize again. My only experience with a diesel has been my '91 F250 with the 7.3 IDI. That was a massive learning experience, and frankly a huge part of what gave me the confidence to buy an old diesel Kubota. With my IDI, the glow plug "Wait to Start" light runs for about 15 seconds on a cold engine, the light goes off, and I am good to start the engine (down to about 0*F). Yes, it took me a lot of work to get that old IDI to that point.
The thing is on that IDI, I believe those are traditional glow plugs. While the WTS light goes out, the glow plugs are in fact still energized for a few more seconds, and then will cycle for a few seconds after that. This is I believe a system to reduce emissions per the EPA or California or something. It has the secondary benefit of leaving glow plugs that are still burning hot while the engine is cranked over.
At any rate, the L35 has what are called a "Super Glow Plug". Per the WSM, the glow plugs should have a 5 second or less warming time for any temperature in which I will attempt to start this tractor. That is, 5 seconds, at -15*C, and what I believe is called an inverse bell curve for time with increasing temperature. This leads me to believe the glow plug controller, and the coolant temperature sensor is in fact working correctly.
I say all this as it appears these "Super Glow Plugs" may stay hot after the relay clicks off and the glow plug light goes out. They do not need to stay energized while the engine starts, as they stay hot. That said, this is what I reference as a potential secondary issue above. My secondary issue concern is in the WSM, on page 9-M9 "Function, Step 3", it seems to suggest that the glow plugs are reenergized when the key is turned to "Start". It is possible that my struggle to start when cold is possibly due to the glow plugs not being reenergized when the key is turned to "Start". This is something I can check tomorrow. I'll pull the L35 in the garage, let it cool, pull all the covers off, and read voltage as the glow plug bus bar while the engine is being turned over.
I do have an issue, where the key no longer shuts the engine off. This may be a failure of the engine shutoff solenoid, wiring issue, or ignition switch issue - I haven't had time to diagnose this yet. If it is an ignition switch issue, it is possible that the potentially faulty ignition switch is also causing what may be the secondary issue described above.