You may now want to consider your general approach. Are you setting-up a challenge, that they either resist or feel they cannot live up to? Are you being too permissive, or too direct?
You can switch to another induction, such as another handshake, or something related like the 8-word hand-drop. However, if you choose to use a non-arm-based induction (perhaps because your confidence has taken a slight temporary dip), you do not want to switch immediately as it will give the impression that things have failed irretrievably.
Instead, pick up their heavy arm by the wrist, shake it slightly and say something along the lines of:
“In a moment, I am going to let go of this heavy arm. And as I do so, I want you to allow your eyes to close as you go inside and relax.”
[Lift the arm slightly and then drop it by their side. If they do not close their eyes, go direct and say:]“So, go ahead and close your eyes as you go inside and let go of any stress and tension.
“And just carry on breathing in that way… [said on the inhale] breathing-in peace and calm and [said on the exhale] letting go of all stress and tension…”
[If they did close their eyes, carry on by saying:]“In a moment, not yet, but in a moment, I am going to pick-up your other arm, limp, loose and relaxed, and when I do, you can take a nice deep breath. Then, as I let go, you can go even deeper into that relaxation, letting go, floating, drifting deeper down…”
[Pick up their other arm, shaking it slightly slowly from side to side. If they do not take a breath, say, “now taking a nice deep breath.” Then let the arm go and regardless of their response, say, “That’s right…”]“And I would like you to take a moment now to simply be. Your subconscious is learning to work in new ways, for your benefit, and there is no need for us to rush that… So, when you are ready, when your subconscious and conscious mind are ready to work together to embrace new learnings, employ fresh resources and take you to new depths of experience, you can open your eyes and we will continue…”
You are now in a better position to carry on with any induction you choose. As inductions with a strong physical element have not yet signified success to the two of you, you could carry on deepening the relaxation with a simple progressive muscle relaxation. Another way to proceed with their current level of relaxation and morph it into a hypnotic induction, would be something like Dr. Flower’s Induction.
However, my suggestion, depending on why you feel they have not responded as expected, would be to opt for an induction without any element of binary challenge or failure. I am not in your shoes, so it is difficult to judge the impact of the previous non-successes, or to ascertain how well you have re-framed them as feedback to discover the best way to work with their powerful subconscious mind. Nevertheless, if you sense any feeling of failure on their part, or scepticism of your abilities, it would be wise to avoid switching to an induction that has a succeed/fail element to it, e.g. an eye-lock or arm-levitation. An obvious example would be something like the Leisure Induction.
If you act smoothly and confidently during this entire process, then you will often find that your partner presumes all of the handshakes were merely information-gathering techniques. You, however, know that they eventually became useful pre-frames and provided you with a workable level of relaxation before you even began your ‘real’ induction.