Obviously, you have the older Compur Shutter - Hoo... "M" synchronization for class "M" flash bulbs... and the "V" self-timer.
Remove the back and observe what happens. It sounds like you are pressing the cable release, or the body "pre-release" - the two "shades" immediately in front of the film plane open, and the mirror flips up and out of the way.
Those "shades" will stay out of the optical path only while the pressure is maintained on the shutter release.
Try setting the shutter to 1 second. With the back off, observe what happens when you depress the shutter release and hold it for a couple of seconds. Then rewind and "jab" the release quickly... It is easy to cause these two shades to close prematurely... resulting in an exposure much shorter than 1 second.
I think that is what must be happening with the self-timer - the "shades" close before the shutter fires.
Check you camera. There should be a little lever at the shutter release button. Normally, this lever is left vertical - no effect. When rotated "outward" and the shutter is tripped, it will keep the "shades" open until it is returned to its vertical position.
I hope this makes sense ... I've re-read this a bunch of times ... It's a whole lot easier to do and show than it is to write about it.