Some things to check
Drain and lubricate the air locker pistons, its not in any of the military manuals but I started a thread long ago with info
https://www.steelsoldiers.com/showt...l-you-differential-lock-cylinders-on-your-SEE
Check the alcohol tank. The cap sits slightly above the back deck and frequently folks have stepped on it and smashed it in. If this is damaged it could be full of dirt. If the valve on the alcohol injector is closed make darn sure you don't open it if there is dirt inside the tank its direct shot into the air system. I think most folks just remove the tank and not use alcohol which is only needed in freezing conditions. Alcohol injection for brakes is definitely not great and if you do plan to use it in cold conditions consider installing an air dryer. I have the parts to do the swap but haven't done it.
Check your cross body air line with a magnet. This runs from the back side of the air pressure regulator on the passenger side frame rail to the air manifold in front of the air tanks. Use a magnet, if its steel swap it out with either stainless of cupronickel. If its steel plan on taking the air system apart to clean the rust flakes out. The line rusts from the inside out so it may look good but its big known source of contamination. The military had a technical advisory and they swapped it with stainless. Note the fittings are metric AN fittings, Belmetric is a source (and also own a Unimog (or two)).
Speaking of technical advisories, it you search around on the Misc Tech manuals forum on this site you will find a collection of military service and tech tips in one thread that would be useful to go through and there is more recent thread that has a student handout for SEE mechanics that has some nice diagrams and explanations of systems.
Take a thin stick and spin the hydraulic cooling fans, they should run free with no friction. There is s known defect that the wires were routed through the top of the cases and the rubber grommets fail due to sun exposure. That lets water in the fans and either shorts them out or rusts the guts. The military fix is just smear RTV on the grommets. I think the field fix is cut the wires. The fans only run after an extended period of running the backhoe so next time you are using it for heavy digging check that both fans turn on. If there is short it will blow a fuse that takes out the rear platform mounted controls.
My last recommendation is get few tubes of grease and a good grease gun and go through the entire lubrication schedule on both the chassis, the backhoe and the loader. Some grease points are hard to find but they exist. On the backhoe some are hidden when the backhoe is stowed. The original grease can turn gritty and solid so its best to follow the instructions on greasing and get fresh grease in every joint. The worst one to find IMHO is one on top of the transmission, the only way I could get to it was rotate the backhoe up and then crawl behind the cab and reach down to find the zerk. Note the instructions on not overlubing.
Good luck and hope you got a "good one"