I have a healthy emergency fund.  

(I'm assuming that's considering for vacancy, % of insurance deductible for the property, cap ex/planned upgrades, and emergency repairs - how much?) 

Common responsibilities include tenant communication, finding tenants, collecting rents, handling maintenance calls, facilitating evictions, coordinating regular maintenance such as landscaping and ad-hoc maintenance such as getting units ready to rent or emergency service like plumbing and HVAC.

They didn't exist when the law was written, and probably emerged as a response to the FDCPA.

@Gene Hacker  the lesson here is proper procedure when tenant dies... yes there is one, and if it had been followed you could have protected your property better.You are not required to turn over any property to anyone without confirmation of whom is the deceased estate representative, A landlord responsibility is to secure the unit, change the locks, and post on the door that keys are available from management,notify emergency contact that this has been done if there is one,  and release property to representative with that has proper authority to take deceased's property,, the estate is responsible to pay you the landlord any unpaid rent, and give notice for termination of occupancy. 

With that said, an investor should already have a good emergency fund set aside, so the allowance taken from the rent proceeds is just extra padding, correct?

CAP rates in San Francisco are really low, which means that a regular 20% down payment will give you negative cash flow.You should buy in an emerging neighborhood with high appreciation potential.

Before you start saving too much to invest, make sure you already have emergency money put away so that you never get taken out of the game. 6 months of living expenses socked away out of sight is a healthy amount.Once you have that (and not sooner), you've probably heard this already, but pay yourself first.

Then emerges Biker Dude's other ex-wife who had previously signed a quitclaim deed but not the right KIND of quitclaim deed (and now that there was money involved, didn't want to sign the new deed without getting some of the $$).

I know the ideal is 20% but I would like to keep some cash for emergencies.