I have the same issue as the OP. I completed the basic training, did the 1st 3 tiers of the combat spec, received the advanced training mission, completed that, received the combat spec choices, selected Engineering, then after completing tier 3 of engineering, got the dialogue to select 500 UPs or a new spec, but the spec menu did not appear, it just passed straight on to the tier 4 engineering mission. Is there anything I can do to manually fire the specialisation or UPs selection menu? (If I select any other specialisation I just get the Unlock check and cant do anything more to advance the missions)

Ah. Hold the phone. I went back through the discussion and found a KnowitalDM comment from January "@Nasaman, to unlock a second (or third, etc) Specialization, you must complete the Advanced Training (which is unlocked at Rank 3 of any Specialization), or complete Rank 5 of any specialization. You will be asked during this to select either to unlock a new Specialization or gain 500 UP. If you select the UP, you cannot unlock another Specialization unless you complete another PDA mission at Rank 5."

I take this to mean that the 1st specialisation unlock choice happens at level 3 and then all the others happen at level 5.

If this is correct then I was confused by the level 3 message on my 2nd specialization telling me I could select another specialisation or 500 UPs.