@Jacob Mallison I'd say the best thing you could do for a Realtor is to provide leads for your clients that want to transact real estate.We're always looking for leads - especially those from referrals.You might not know this, but in most, if not all states, it is illegal for a real estate licensee to pay any kind of referral fee, finder's fee, etc to an unlicensed person.That said, if you want to find a good agent, look for someone who is full time and hungry.

It will also go towards your further required education as a licensee 

The Agency’s investigations are complaint driven, so we rely heavily on the public, and our licensees to bring these individuals to our attention.

The Division of Real Estate in my state is taking a good look at wholesaling right now, and word around the campfire is they are looking really close at licensees who also wholesale.

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.