Scottoiler won't work unless engine running as it relies on a vacuum generated from the engine to " power " the unit. If the oil is dripping when the bike is stationary it must therefore either be coming from excess scottoil delivered when riding, or otherwise from an oil leak.
I remember Elvie had a similar " leak " while we were in Hungary this year. She normally runs the unit at approximately half the rate specified in the instructions, but had turned it up as she had to prime the unit because she had run out of Scottoil. ( see blog for full story ) One morning on routine checking there was a small puddle of oil under the front sprocket area. After checking oil level she decided it was due to excess Scottoil, turned the rate down, and no problems since.
If you are worried about running the Scottoiler at a lower rate than specified I would point out that we have run the units on various bikes over the past 10 years, and after finding Scottoil on a couple of rear tyres when first adjusting flow rate we settled on our current rate of one drop every 2 minutes as opposed to the recommended rate of 2 drops every minute. As yet we've not needed to change chain or sprockets on any of our bikes. Elvie's blade is on 25,000 miles or so, and the chain and sprockets are fine.
I'd also point out that all the above relates to road riding only, I suspect that offroading would require a different approach.