When running, the d24 injection pump needs constant 12Volts supplied to it otherwise the fuel shutoff solenoid will activate and block a running engine from running And similarly it would also block an engine even from starting (if no 12V to IP).
I am not sure this is helpful info in your case but worth a try seeing the pin on the IP and trace/track the routing of that wire and make sure your engine has perfect uninterrupted 12Volts (
when the key is turned in position II , or/and when running).
The movement of the pedal is in relation to how much vibration is created (because of variations of engine rpms) so IF a bad wire is failing this could be affecting how/when/if the engine runs/cuts off. I would start by making sure that the 12V is constant and intermittent to the IP ( supplied when engine is running and/or when key is turned to II)
You can remove the pin and manually supply 12V using a wire that safely connects the battery and the IP, only to see if that was the source of the troubles of staying running.
(If fuel filter condition/age is unknown or if bad quality of fuel is suspected, you could also just add a new fuel filter anyways; but I doubt a 'clogging' filter is causing the symptoms you are experiencing... About water in fuel. I have never found water in my filters but you can use the drain under the filter to see if there was any... ... with these cars what's in fuel is usually AIR, not water
)