There are three options:
1. The health of Jackson's father improves. In this case the health of his father will cease to be a reason why Jackson cannot make himself available for a few hours of testimony before the Royal Commission.
2. The health of Jackson's father lingers at the present state. In this case Jackson will presumably find away to continue carrying on with life and will no longer have to holed up wherever he is, which would mean Jackson should be able to make himself available for a few hours of testimony before the Royal Commission.
3. Jackson's father expires. In this case the health of his father will cease to be a reason why Jackson cannot make himself available for a few hours of testimony before the Royal Commission.
If Jackson leaves Australia without testifying before the Royal Commission and does so despite the Royal Commission desiring to hear his testimony, the his departure will be nothing short of fleeing the jurisdiction in order to avoid giving testimony in public and under oath.
And, unlike what Watchtower's attorney has said, there is a caveat to Watchtower's Theocratic War Strategy doctrine having to do with testimony given under oath. Under Watchtower doctrine once a JW places him or herself under a sworn oath to tell the truth then WHATEVER they say has to be true. To put it another way, once a JW places him or herself under a sworn oath to tell the truth Watchtower doctrine forbids them from offering deceptive testimony.