Does that engine have an oil pressure relief valve of some kind that might be stuck open? You could remove the oil pressure sending unit and turn it over to see if oil squirts out the hole.
I'd at least get a diagram of the oil system on that engine and look at it to see all the possible failure points before dropping the pan to replace the pump. It seems very odd that a pump would fail from just sitting. It seems more likely to me that the problem lies elsewhere.
1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13