When the servicing was done, I spent some time figuring out how to remove this f*****g self-timer mechanism, and lost some time fetching the Internet for some tutorials on this subject. After a more thorough examination, I found two JIS-00 screws at the bottom of the mechanism, and was sure trying removing them would not dismantle the delicate thing.
It came surprisingly easily, and with no interference with the rest of the camera.
The mechanism by itself is very neat, and seems fine.
I tried dropping it in IPA for a while, then played with it a bit and this seems better. I had fears that an axle was broken and this could be the cause of the jam, but my personal mechanical expert (aka my son) decided this is by design that a part of the mechanism can move out of its normal position so that there is no need to repair this. I'll trust him on this.
The IPA helped getting the timer getting back to _some_ movement, but it does not go to the end, so I suspect I have to dip it longer and lubricate afterwards.
Anyway, I decided I wanted to know if the camera could do without it so that I had a plan B.
Putting the mirror box back on is... interesting, particularly as I did not take care of the different mechanical parts, so I had a half-jammed camera. The tutorial is very well made, but I had to find a way to put the "mirror up signal pin" in the right position, and to do without being able to wind the shutter halfway since it was wound and would not trigger as some levers were not there to allow a proper cycle.
To get the "mirror up signal pin" in the right place, I found the easiest is to push the mirror up gently so that the lever is in the right position when putting the mirror box back.
The current situation is that the camera fires again (hourra!) at all speeds, proving the selftimer is not needed if I can't get it back to proper operation.
Next issue is that I have to find why the winding mechanism will jam from time to time, and need to remove the winding lever to unjam... I suspect some gummed-up grease at the bottom may not help, so I guess the next endeavour will be to dismantle the bottom of the camera and its mess of a gazillion levers. This will be a task for a day when I'm home alone, I guess!
In the meantime, I finally ordered some tools (a spanner wrench is much needed, as a minimum) and some new leatherette to that the camera can look nice WHEN I get it back to work!
Another issue is that this is becoming addictive, and I'm already looking for the next project (and I know ADHD is not my ally here, so I try to resist...)