Air carrier Captain reported confusion over NOTAM clarity and an ATC clearance resulted in an incursion to a closed taxiway at HNL.

Narrative

We were cleared to taxi by Ramp Control from our parking via Taxiway V to hold short A; and contact HNL Tower 118.1. Tower and Ground were combined on 118.1. Immediately after contacting Tower and saying we were on V to hold short A; Tower said Hold position and who told us to taxi on V. I replied ramp said to taxi V to hold short A. Tower stated hold position he would call them and that we may need to be towed back to ramp because A is notamed closed. After a while Tower called back and said they are working to get clarification. I said OK; I believe per notam that we would be able to taxi on A to J for the right turn on J. He said A was notamed closed. We continued to hold position. Meanwhile we saw lots of airport vehicles come lights all flashing looking at situation. They got all the work vehicles and barriers moved clear of what you will see highlighted in red on airport diagram. Then Tower told us to taxi V; A to cross 8L to J to hold short 8R. And that is when it became clear that there was confusion as to what part of A was closed in the notam and the other closures of T. And the way we as a crew interpreted the closure was what is highlighted RED; but we were seeing while waiting that since A split at V where we were coming to the right for the closure and could have gone straight passing A4 and A3 and then a right turn from A onto J to then hold short 8L. Versus what Tower was interpreting V; A; cross 8L to J; (which this required all the construction equipment to be moved). Once all clear and double checking clearing to taxi and how were would proceed to comply we taxied and no issue.Cause: We think the confusion comes from the fact that A Taxiway makes a split/turn right at V. And that the NOTAM could be clearer if stated A closed at Taxiway T south to J.Also not able to really ask any questions because Tower was busy with inbound and outbound traffic and taxiing aircraft and doing such would have taken to much radio time he needed to work traffic.Suggestions: The NOTAM could be clearer if Taxiway A make the split/turn by saying A closed from T south to J. Or renaming the A part after the turn to something else.