It would be more usual to spin up a task to handle the request immediately rather than having a task sitting spinning its wheels until a request comes and and triggers it into action.

If the triggered task is long running and you want to decouple it from the response handler for a page have a look at some of the results in the following super search: ?node_id=3989;HIT=long%20running;re=N;Wi

Otherwise, describe your big picture problem so we can help with that rather than help with implementing a solution to the wrong "answer".