I asked a Yellow Jacket Rep this very question. He said as it will not hurt to store it without oil (except as stated above, more chance of moisture contamination) to store it with the oil and change when you first start it. Now keep in mind he was a sales rep. I was wondering if storing it with oil for long periods if the oil would sludge up or gel. That being said my pump is on my truck year round with oil in it and I never had a problem starting it, besides the chug you get from a cold start and I open the gas ballast.
You need to put the phone down and get back to work!
I would want oil in it all the time...thinking moisture/condensation too......although, Mine gets used frequently year round, so never had a "storage" concern.
I have never seen any issues with moisture at all, but that being said, we have pretty low humidity here.
One thing I do is keep a 1/2" PVC cap over the end of the handle (this is where I have a lock out tag so when it gets used the tag is attached to the cap).
The reason I started doing it this way is time savings. I can empty the oil while on the call I just used it on and refill it on the call I am using it on next. Don't have to wait for it to drain.
I keep two pumps on my truck, I have a JB 7 CFM and a JB 5 CFM, this is why sometimes I can go months without using one or the other. Often time end up working on two systems at the same time, soooo..
The 5CFM JB is almost 12 years old.... Has virtually never been stored with oil in it, that being said, it was empty when it came out of the box new.
I work commercial and can work on anything from a three ton gas-pack to 2500 ton centrifugal chillers... I also do quite a few built up systems, so when I do use my pump(s) it can be for several days at a time.
The oil is just mineral oil and is very hygroscopic, so the only way to keep it really dry is a closed container (which a vacuum pump is not), heated or under vacuum. Just made sense to me to make it go away.
If a day goes by and you have learned nothing, I hope you got a lot of sleep.