With most shutters the 1/8 second is usually the first slow speed to engage the star wheel pallet, so it does sound like an escapement fault. Although, escapements that are sticking usually tend to manifest more as speeds decrease, hence, it's most often the one second that stalls, not the 1/8, as the gear train has to be wound further for a second, to give the maximum delay, than it does for 1/8.
In your case, with 1s, 1/2, 1/4 etc. being OK, but the 1/8 running longer, I still suspect the escapement is the issue, but, it sounds a bit like the problem may be that the escapement control pins or levers (I don't speak fluent Nikon, sorry) are not being correctly set for the 1/8 speed. If, as has been suggested, you can see the escapement with the bottom cover removed, I would be inclined to get a light in there, work the speed dial through the speeds from 1/15 down to 1s, and see if you can visually detect the reason why the 1/8 is being delayed.
A few months ago, I had a similar problem with a Fujica ST801: all speeds good bar the 1/8 (which IIRC, was too fast in that instance, not too slow). It turned out one of the control levers that sets the escapement had become slightly bent (ST801 escapement lives under the bottom cover, so perhaps it was dropped, or banged onto a hard surface when it was set down at some stage?). Correcting the bent lever, which had jammed, saw the 1/8 come back in immediately. So I suspect yours should not be a very difficult problem to fix, if you can observe the escapement being set at the various speeds, and in operation, because, to my mind, it's sounding like a simple mechanical malfunction (Ie. worn, loose, distorted, or detached parts) may be the cause. I would certainly investigate that first, before contemplating any adjustments to the curtain tensions which will impact across the speed range. Keep us posted, please. I don't own a Nikon F, but, eventually, I would like to!
Cheers,
Brett
