I had pretty much the same issue with my 94 k1100lt. It would leave an embarrassing puddle every place I parked. Someone(idiot) had replaced the old pump with the new style and did not use any sealer on the mating surfaces! The oil would seep down the wire chase between the cover and the housing or main block. Very hard to see exactly where the oil was coming from.
Yes get the o ring. There is also a smaller one on the shaft that I was told is not really a seal, but helps support the shaft. Both very cheap. Do it while ya got it apart. may as well. then do it just as Robert said.
Clean the Cover, the housing and the engine block surfaces shiny clean. wipe dry with evaporating cleaner.
Get Ultra Black RTV. My local BMW shop mechanic recommended this to bear up under the pressure, oil, and vibration.................so far so good for me(three months)
I used a tiny hole in the RTV cap to lay out a very small ridge all around the center of the mating surface on the engine block with a little help from tooth pick to help level and dab where needed. Go extra light and clear around weep hole as circled in Roberts Pix. Don't want to plug that, but you do need a seal there. Put your o ring in,(or both if you got um, its open so may as well, I would and did both. one is very small and just fits around the shaft).
put it all back together so the RTV is just squeezed enough to be touching both surfaces solidly. (finger or a just a bit more). Wait the recommended time to let the sealer start to cure and torque the bolts/screws. DO NOT OVER TORQUE! These are small bolts in alumimum and will strip very easily. I think it is 7 nm, but don't quote me look it up. Also because some of the bolts/screws are behind the cover...........you may have to do it in two stages if I remember correctly and do the cover after the housing starts to cure? Let it dry for 24 hrs I believe it is. Good to go. Mine has not showed any hint of oil since I did this............DRY AS A BONE. :riding: Lots of good vids on utube on replacing the old pumb with the new parts. Just watch them to get familiar with the tear down which is really pretty easy.
As always.....................I could be totally wrong....................Good luck! (really pretty simple if you don't need to replace the pump)