Why don’t they like their tails lifted? It’s a trust issue.
The only time a female wants her tail lifted is when she’s lying down being bred – a volunteer position. Otherwise she wants that area private, thank you very much, and will spit off anybody who fusses with it.
For a male, it’s even more important. Those nasty fighting teeth are supplied to hamstring and castrate opponents, so you KNOW he wants to keep what’s under HIS tail safe!
Nevertheless, teaching him to have his tail lifted is no more difficult than teaching him to be touched in any other place. Touch his withers, reward. Touch his withers, slide down his back, reward. Touch his withers, touch his back, slide down to his tail, reward. Touch his withers, touch his back, touch his tail, slide down the side of his tail, reward. Keep working.
Don’t think about actually lifting his tail at first, just get him comfortable with you touching the bottom of it. Work up gradually to being able to lift it.
I start this behaviour with the llama tied up. When he’s very good at letting me lift his tail, I start again from scratch with him untied, but I’m holding the lead, as I would be in the show ring when the judge asked to see his testicles.
If you haven’t done a lot of work yet on touching him in hand (with you just holding the lead), you might want to go back to using the whip for a while. When you get near his rear end, he’s going to start moving it away from you. Without the longer reach of the whip, you could easily wind up spinning in circles with him rewarding his spinning by being able to keep his rear away from your touch. With the whip, it will be much easier to keep touching him until he stops. As soon as he stops, reward him by taking it off him.
When he’s figured out once again that the only way to get you to stop touching him is to stand still, you can switch back to using your hand. My hand cue for this behaviour is simply to run my hand down his back, under his tail, and lift (pushing the bone up, NOT pulling the hair). My voice cue is “Gimme Your Tail!”