When I was an airshow performer, one thing I had to get used to was betting "tech inspected" before every show. The FAA airshow monitor checked the pilot and aircraft paperwork and looked at any obvious stuff like placards and compass cards. You get used to it. Your goal is to bore them. Once they have seen you a few times and they haven't seen anything exciting, they look for more interesting targets.
The FAA inspectors instructions on how a ramp check is to be conducted are in Flight Standards Information Management System FAA Order 8900.1 on the internet. There are things that they are directed to do, and there are things that they may not do. If you work with FAA a lot, it is worth your while to read their manual. You can help them stay on the straight and narrow and keep them from going where they should not if you know their internal rules and are diplomatic enough. I think of it as mental jujitsu.
Fly safe,
Wes
N78PS