Currently I am struggling with something very similar.
I had lots of CH attacks (which also triggered migraine attacks) from April and it stopped 7 September. Normally October and November are the most quiet months for me. But not this year. A few weeks after the cluster stopped, I have this constant headache exactly as you describe and exactly on the same places as you show in your picture. But it is not 24/7. I would say its around 3-4 days a week. At night it is much stronger than during the day. Begin November, we had the change to wintertime together with a very big drop in barometric pressure. That headache came then very strong then and resulted in 5 CH attacks in one evening. The next evening I got another 2. Then it stopped but currently again 24 h headache for 2 consecutive days. It feels like a CH attack that started but got stuck halfway and now sits there. Sometimes it comes stronger for an hour and then go back to its base level. I have to go back to the hospital in February and I also will ask a trial for indomethacin. But I doubt its one of the hemicrania as I have excellent response on triptans and oxygen. Normally both hemircania do not react on this.
My CH is in permanent evolution and changes all the time. It has a lot to do with the heavy migraine I had for my entire life but seems I start to grow out of it (I am 50 now) and it is disappearing more and more. Seem the CH does not yet know how to behave with all this room in my head for itself :)
I experienced my first CH in 2012 but it is the first time I have this semi-permanent headache.
I think the best you can do is go to a doctor and ask for an indomethacin test. Your doctor can look up the doses and how to take it (as it is heavy on the stomach many take additional medication to protect the stomach) and then you will soon know if it is hemicrania or not.
You can also search for "shadows" here on the forum. There are lots of threads about this subject and I remember stories from people who struggled with them for months and months in a row so I assume that these symptoms are not uncommon in CH patients. Some patients have clear-cut attacks and others have a migraine-like CH. I read once an article about this and that is because it seems that nearly 50 % of the population carries a migraine genetics but most actually do not have the condition. However, in CH patients, this genetics can make CH showing migraine-like features like nausea, photopobia, slow onset of attacks or long-lasting shadows between the attacks.
I learned one thing... headaches are a complicated business :)