Thanks, everyone, for your responses! I'm finding them helpful.
Part of the problem I think might be that this ISTp is used to talking with me and interacting with me in regard to practical things, not necessarily "fun". Also, he has a (very reasonable) phobia of photos of him ending up in the hands of people who could hurt him or those he loves. He's really, really cautious of having his photo taken so I think that adds an even greater level of stiffness. (He was in special forces.)
He's very much one of those closed off to people (particularly emotionally) unless and until he knows and trusts them. Happily for me he seems to be growing more trusting of me, which I take as a big compliment. But there's still a ways to go with that, I think.
Not being the most emotionally expressive person myself, when I'm taking pictures of people in general it takes effort to generate the atmosphere that gets people to smile. Those suggestions of joking with him, gentle teasing, talking about enjoyable things, etc., works great with other people in general, and they'll probably work with him, maybe I'll just have to be patient and persistent with it...
It's so hard to generate a natural-smile-inducing atmosphere with an Fe-PoLR!
That must be my problem.
Not hot enough...
Actually, I gave her the camera at one point and she got the best look from him that I've seen yet, though it was blurry and thus unusable. But, yes, that's a good point. I think the greater the relational bond the easier it'll be.