John,
I'd recommend saving yourself the headache and picking up a used one for $500-700 and it is YOURS. You can use it anytime you need to, beyond just NASA weekends. Like when you need to trailer the car to annual tech, or to the muffler shop, or to get it aligned, or whatever. Don't have to worry about when your partner needs it on conflicting weekends.
You won't have to worry about scrambling to load up Friday night only to discover that your partner broke a tail light lens or spliced into the harness to make it work on his "other" tow vehicle.
In sue happy California, you also need to think about the possibility of liability for someone elses' actions with a trailer that you are part owner of.
Buy the trailer for 1/2 price of a new one and you are ahead after a season when you factor in rental costs and extra time involved in picking up/dropping off the trailer. Keep it for a few years and you're miles ahead.
I crewed for a Rally team that borrowed a trailer before every event....what a pain for them that was.