A client contacted us a while back with TMJ hypermobility. Problems chewing - laughing hurts, etc - here is our advice.
The TMJ is very unique and a complex joint - and I totally understand your approach to laughing !!!
Logically to get a bit more protection and support in the end range of motion - the position where you luxate or sub-luxate the TMJ - I would apply the tape with some stretch (maybe 50%) distally to proximal. The tension I will encourage you to adjust to your own liking. Furthermore - I just want to make sure that you do apply to both sides as tape only on one side can shift your bite.
By the way - have you been advised to less chewing because of joint-changes ? In my opinion - chewing is a controlled motion in mid-range and therefore a good exercise to strengthening the chewing muscles. The stronger and shorter they are - the better control you will have over the TMJ. Just a thought !!!