When Agent places call on hold (he presses hold button on phone and we see his state ‘OnHold’ in queue)
Queue does not think that it is empty and waits till OnHold ends.
Any chance to make Queue see OnHold state like InUse?
What you need is a queue Pause - it should be trivial to set up with a specific extension.
Oh, could you explain please, how can I map phone side hold function with asterisk’s pause?