I have been looking online and have been unable to find out how long it usually takes for the state to approve a new licensee.  

Do you have any recommendations on an agency that would sponsor me on the licensee knowing that I'm not going to be actively working as a buyers/seller's agent other than on a limited part-time basis?

You are a licensee... 

If you purchase, make sure and put in the contract that you are a licensee.

Deal with a licensee on a listing,,,use standard contingencies to protect yourself.

Actual pics of recent solds, actives and pendings with a location map.From my average schmuck, non-licensee position, Zillow and Redfin are good tools to have.

HI Roxanne,It is true you need to be in the business for 2 years but no one talks about the details about how that is documented which is either by:- Looking up CA BRE website consumer licensee information which will show how long you've been licensed- CPA letter to sign/date on you being self employed for 2 + years or 5+ years if you're using Freddie Mac's program since Freddie specifically wants 5+ years to use 1 year tax return- or another third party to verify you've been SE (self employed) like business licenses, attorney's, other auditor or licensesWith regards to income like others have mentioned you can use 1 year tax return to base your monthly qualifying income off of.Freddie mac, like mentioned above is a a conventional financing option but the downside with Freddie is they want 5 years in the business as documented with one of the options above.

And I must also provide a disclosure of self-represented agent licensee and financial interest. 

For instance West Virginia has a reciprocal agreement with Virginia....but will refuse to issue a license to a Virginia licensee that lives outside Virginia, even though no law or regulation states that they can or will do that.

The exemption is never extended to real estate licensees or professionals.Also while the exemption applies, it does not necessarily protect you from civil liability, as there have been a number of lawsuits in the last few years against AirBnB and its host regarding the Mrs Murphy exemption.