Hi John,
Glad you stopped lurking, but it's unfortunate it happened because of a problem with your watch. To explain this requires some understanding of how the hour counter works. Unlike the minute and central chronograph seconds, which are driven off the 4th wheel of the movement, the hour recorder is driven off the mainspring barrel.
Here is a shot of a Cal. 861 showing just a few parts installed on the dial side:
I have added some labels to help with the parts:
A - mainspring barrel
B - friction spring for driving pinion
C - driving pinion
D - hour recording runner
E - hour hammer
Here is another shot with more parts added:
F - hour recorder stop lever
So looking at the first photo, as the barrel A turns and the watch runs, the driving pinion C, is coupled to the barrel only by the friction spring B. The silver coloured circle in the middle of the driving pinion is the barrel arbor, so the post that the barrel spins on, and this arbor only turns when you are winding the watch (in this type of design it's the barrel that turns when unwinding, not the arbor).
The pinion C on the barrel meshes with the hour recording runner D, and this is the wheel that the hour recording hand is mounted to. The hour hammer E is what resets the hour recording runner, as there is a cam on the underside of runner D that can't be seen in this photo.
If you now look at the second picture, item F the stop lever is what holds the runner D in place, and keeps it from turning all the time. When people see "hour recorder creep" on a watch, it usually means the stop lever F is not engaged firmly enough to runner D, so the hand runs even when the chronograph is not turned on.
The driving pinion C is only coupled by friction using spring B to barrel A, because most of the time under normal use the chronograph is off, so the barrel spins and that pinion just sits there stationary until the chronograph is started. Also, when the chronograph is reset, the runner D spins rapidly, and it actually causes the pinion C to spin as well, but it does not have any effect on the barrel because it's just friction coupled.
So if you were able to follow that background, now onto the two problems you are seeing, and they are somewhat contradictory. Now if you follow how the hour recorder works, you see that if the hand gets jammed on the dial or something, it won't stop the watch - the friction coupling just decouples and lets the watch run as normal. So any kind of interference with the hour hand can cause it to stop working and the remainder of the functions will work fine. So I can't say why your hour recorder doesn't always run.
Now you say it spins directly proportional to how you wind the watch, and if you recall above I said that the barrel arbor turns when you wind the watch. So it would seem that the pinion C is somehow caught on the barrel arbor, and it's caught heavily enough to drive the runner D, and overcome the braking action of the stop lever F. To me this implies some sort of burr or something maybe on the steel barrel arbor that is digging into the brass pinion, catching it, and making the hour recorder spin as you wind. But if it was hung up, then the hour recorder should run almost all the time, so maybe this catching is intermittent.
Pretty difficult to say for certain what the exact cause of this is, but there's no doubt the watch is faulty based on your description. Not sure who the seller is and what their return policy is, but I would first contact them and see what they would offer in terms of a replacement, refund, or partial refund, as this watch needs to be looked at certainly.
Unusual defect with the hand spinning as you wind the watch - can't say that's one I've come across before and I've serviced hundreds of these watches...
Hope this helps.
Cheers, Al
