By the way, the electrical schematic in the student handout is low resolution and has a fold in the center. Look up this link https://www.steelsoldiers.com/threads/unimog-flu-419-see-wiring-diagram.168054/
Its a much higher resolution. Transfer it to thumb drive and a local Staples should be able to print it out full size.
Things that should be on you priority list.
Remove the bleeder plugs from the two air tanks and the bleeder that sits between the two air tanks. Remove any crud that is in there.
If there is a lot of crud in your cross body air line its probably rusting out on the inside. It runs from the regulator on the passenger side across the body to the air system. If its stainless its been upgraded, if it steel it hasnt. Do yourself a favor and swap the steel one out.
Take a look at the hydraulic cooler fans on the back deck. Look at the fan motor enclosures and see if the electrical wires entering the enclosures are coming out the top of the enclosure. The seal into the enclosures tends to crack and leak water into the motor enclosures which eventually short out. You can take a thin object and try to spin the fan blades to see if they are seized up. If they are still spinning put some RTV on the connections to try to seal them up. Just because they spin does not mean you are all set but is a good sign. If at a later date when you are using the backhoe and the fuse blows that feeds the rear deck they you probably have a shorted out cooler fan. Its tricky one to diagnose as the fans have temperature switches in them so everything will be fine until you are using the backhoe long enough for the fans to try to turn on. By the time you stop and try to figure out whats wrong, the fan temperature switch is open so the system tests fine. (Been there done that a few times)
Open up the drain plugs on the diff locks and spray WD-40 up the drains. The Technical Manuals do not show this service and on mine and I think on many SEEs the plugs are painted over. I posted photos long ago on a thread. If the diff locks are seized the parts are cheap but axles need to be disassembled.
If you are ordering parts, order two nylon shift bushings. The long thread had a couple of descriptions and photos of how to do it. When they crumble you cant shift the SEE.
Obviously do the round the truck greasing routine called out in the operations manual. All the fittings are there but some are hard to find. One of the them can only be reached from behind the cab with the backhoe deployed.
Drain the portal axles and replace the fluid with synthetic. Make sure you fill them up per the manual.