Ignore the "pulse width" codes (312, 313, and 315). A DDEC I will set 'low voltage" and "injector response" codes when they are running perfectly. Those won't shut the engine down. They may indicate issues, but they'll likely clear up once the bus is run a hundred miles.
The sensors for both low and high water are removed....? Right?
Is the low water module still mounted next to the ATEC ECM? Small black module that probably has "low water" logo inprinted on the unit. Maybe 3" by 2"...
The low and high water sensors have probably been shunted. I'd try to locate the wiring terminations and see what the PO did to fool the DDEC unit to ignore the coolant sensors. I would recommend repairing the low water senor by installing a low water sensor. Might need to find a plug.
The DDEC manual you've ordered will give you details on how the system works and color codes (numbers) so that the wiring can be traced.
If you replace the coolant sensors, be sure that the surge tank is grounded. It had a wire that grounded the tank to the frame member to the left of the tank.
No matter what else is going on with the cooling system (maybe nothing), the low coolant code problem must be repaired. The bus won't go with a low coolant code set. It can be made to operate for 30 seconds by holding the 'Override' switch located to the left of the ignition master. Has a red bomber door cover.
As mentioned, the cooling system could be checked for sudden increase in pressure when the engine is started. There's some expansoin due to normal engine heat, but the pressure should not suddenly begin to rise. The engine will idle all day without a rad cap.
It'll run down the highway with the cap loose too....don't ask how I know this..
The radiator fill cap isn't a 'pressure' cap anyway.
Overpressurization of the cooling system on an '87 NJT MC9 is handled thru a pressure relief valve mounted on the surge tank. Upper LH (looking at the tank) so don't waste a lot of time hunting for that oddball fill cap.
There's also a small pull valve that releases whatever residual pressure may be in the cooling system when adding coolant to a hot engine. It's located just below the filler. If you see water oozing on the curb side bumper, the valve is stuck open. Just push it in.
BTW, on an unrelated subject, your coach has a transmission retarder that should be 'ON' unless
operating on wet or slick roads. The retarder is controlled by a switch with a bomber cover towards the rear of the drivers side switch panel. When turned off, a light may light up on the RH front (above the RH headlights) of the coach. Probably doesn't work, but that's what the little jeweled light above the RH headlights is for. My understanding was that the supervisors could monitor the use of the retarders by looking for the light.