Rebound headaches

Does anyone know how long a person has to be off the offending medication before any relief (if any) is seen?

It depends on what the offending medication is and how large doses were taken as well.
But for ordinary over the counter painkillers if not taken to excess, it can be only few days, maybe a week, sometimes two, if taken more frequently.

Whatver it is, it might be best to do it with a support of your neurologist, as they might also suggest what you can take to help with the withdrawal (like injection DHE45 for exapmple). You can also ask to have it done as an in-patient in hospital, in case you have a bad reaction.
Good luck, whatever you decide.

I was stuck in a cycle of rebound for a long time, and never knew it until I decided to try a medication holiday. I would say it took about 2-3 weeks before I really started seeing dramatic effects, though I was already starting to feel better about 10 days after I stopped.

Same for me - took about two weeks and then I felt much better.