Like F14 wrote, your combination pump is mechanical—pumping when the engine is running—and your description of the K1100 pump indicates that it probably had a temperature switch installed then wired to a gauge, that’s why there are two wires instead of just the single wire from the oil pressure switch. What kind of liquid is leaking from the unidentified switch every three seconds—coolant, oil, or a mixture of both—and from what part of the switch is it leaking? Have you tried loosening the leaking switch then retightening it slightly more?
How much oil is in the bike? If there is sufficient oil in it then the oil pressure indicator problem may be from the switch wiring, or the replacement pump’s oil pressure switch is seized. You could substitute your old pump’s switch for the one that came with the replacement pump to see if that shuts off the light, and you could remove the unidentified switch replacing it with the plug from your other pump to stop the leak—both tactics that you already have suggested.
If the switch and plug substitutions don’t shut off the oil light and wiring is ok, your old oil pressure switch may also be defective, the replacement pump may be defective altogether, or engine bearings may be failing.
Which manual are you using for guidance?