Its not the low pressure pump if the resorvoir is full. Here is an except from the Dieselmanns webpage:
No/hard start hot or after stalling, usually re-starts after cool-down; Jerky, irratic idle; Possible DTC#'s P1211, P1212, P1283:
Usually caused by low injection oil pressure or regulator (IPR) valve. High pressure oil is used to pressurize and inject the fuel into the cylinders--each injector is essentially its own injection pump. The IPR is a by-pass valve that controls the high oil pressure depending on demand. The ICP monitors the oil pressure in the LH head.
Check for oil in the upper reservoir; it should be within one inch of the top; add oil as necessary. Verify that the correct oil is being used (see my PowerStroke Page for oil specs) and that it is not thinned out.
For no-start concerns check Injection Control Pressure (ICP) sensor readings with a scan tool or pressure gauge (500 min), or with DVOM at pins 87 to 91 (.83volt min) while cranking.
By using adapter fittings and plugs you can isolate and measure each cylinder bank to see if there is a high pressure oil leak in one head, or connect both HP oil pump hoses to the pressure gauge to measure pump pressure. NOTE: The 98.5 and later HP oil lines have special couplers requiring special tool 303-625 to disconnect, and tools 303-627 and 303-628 to connect to the coupler along with a pair of F4TZ-9N332-A elbow fittings to adapt to the HP oil gauge hose.
If isolated pump pressure is low, short break-out-box pin 83 to ground to run IPR valve to full duty-cycle. If the pressure comes up (3600 psi) replace the PCM; if it remains low, remove and inspect the IPR o-rings for damage; a kit is available if they are. If the IPR o-rings are undamaged, replace the IPR valve. If there is still low oil pressure, replace the HP oil pump.
If isolated HP oil pump pressure is 500 psi, or only one bank reads low, remove all the fuel injectors and replace their o-rings using the latest kits P/N F8TZ-9229-AA.
If the concern is a jerky, irratic idle when hot, unplug the ICP sensor (will set a code, causes the PCM to default to a pre-selected IPR duty cycle) to see if it the idle stabilizes. If it does, check the ICP voltage with a scan tool or breakout box at pins 87 to 91 with the sensor plugged in and the key on/engine off. It should be .20-.25 volts. If the base ICP voltage is within specs, replace the IPR; If not, replace the ICP and retest.