I may be inclined to do a free assignment: It depends on what other concessions you have to offer, such as having enough food to consume in the house for the entire duration of the assignment, and auxiliary use of a car as well.
May I please introduce myself? I am a local Los Angeles-based traveling single male pet/house-sitter. I am available all and any dates, I do have a reliable car, and I possess an excellent sense of navigation. I do not mind traveling a bit beyond L.A., or even across the country, as I have traveled quite a bit in the past year for various other house-sitting assignments. I am also a skilled and knowledgeable life-time classic car enthusiast and mechanic, as well as an honorably-discharged U.S. Army Veteran. I am able to provide a wealth of credible general character references, as well as actual house/petsitting-specific references, upon request, relating to assignments done in the past 12 months. I have never been arrested, I have no criminal record, I do not drink, I do not smoke, and I have never had a drug or alcohol problem, and all this can be reasonably-established through a background check of me. I also have a current, valid Police Clearance Letter in-hand, generically-known in other forums as a "police check", from the Los Angeles County Sheriff's Department, to prove my clean record. I am who I say I am, and I am a trustworthy person of reasonable and sound mind. I anticipate your reception.