The oil sender can short and fail. Fairly easy to replace but Unhook the battery first. The starter is right below where you are working and the main B+ stud is uncomfortably close. You will only lose about a teaspoon of oil so you do not have to drain the oil to replace it.

There is not a low oil pressure light on the 124 implementation of the 603, not sure if they provided one on the 140. There is a low oil level light that goes off a float switch in the oil pan. This is set up switched to ground and fail safe, so if the wire is loose it will show low level. I would go ahead and pick up a gasket for this switch at least, when you do your next oil change, at least reseal this sensor on principle, they seem to leak quite often.

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The OM 642/722.9 powered family
Still going strong
2014 ML350 Bluetec (wife's DD)
2013 E350 Bluetec (my DD)

both my kids cars went to junkyard in 2023
2008 ML320 CDI (Older son’s DD) fatal transmission failure, water soaked/fried rear SAM, numerous other issues, just too far gone to save (165k miles)
2008 E320 Bluetec (Younger son's DD) injector failed open and diluted oil with diesel, spun main bearings (240k miles)

1998 E300DT sold to TimFreeh
1987 300TD sold to vstech