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I think in that sort of situation most LEO's are reasonable enough to hear you out if you say, "I'm sorry, sir, but I can't do that because..."
Situation depending, obviously.

I agree with Teamless. If I carry under the authority of the Motorist Protection Act instead of the authority of LTC, I put it in my glovebox. Still within reach, but also secure in the event of a collision, out of plain sight, and easily lockable if I have to leave it in the car for one reason or another.