AS1170.4 Section 7 Vertical earthquake actions 1

In NZ it's intended to be an additional force, additive to other combinations as deemed necessary. An equivalent static vertical action if you like. Suspect the same intent applies for Australian code as you've outlined.

I've never heard or seen of anyone trying to do a vertical modal analysis to apply vertical design actions, it strikes me as being fundamentally incorrect. The derivation/prediction of vertical loading isn't so well understood as the lateral components. Simplification such as vertical period is equal to zero are good enough given all of the other assumptions being made.

In NZ at least, vertical actions very rarely governs over a 1.2G & 1.5Q ULS case since the load case you'd add to would be 1.0G & 0.3Q & E. So the vertical earthquake multiplier would need to be quite significant for it to govern for a strength requirement (basically would need E to be more than 0.2G + 1.2Q to be higher than 1.2G + 1.5Q). SLS governing is a possibility depending on how sensitive your structure is to vertical excitations, but then the seismic actions at SLS are a quarter of the ULS actions in NZ.