I give a quick hi, my role (real or fake), and a brief explanation of what my strategy is with that role. This shows you're intelligent, prepared, respectful of the jailor's role, and expresses eagerness to help the town in general.
For example:
You have been hauled off to Jail
Me: Howdy!
Me: I'm the sheriff
Me: I'm going to check out 7 and 12 next, they've been strangely quiet in chat
Jailor: ROLE OR EXE
Jailor: Oh, okay cool
Me: Give me a code word so I can identify you if I need to
This works with both avoiding trigger-happy jailors, and deceiving town as an evil role. Unless it's late in the game and he's ruled out your role, you'll at the very least buy some days on the clock or confuse the lynch mob a bit.