I agree with Dan, likely metric.  But there are fine threaded and course threaded versions, so if you get them out undamaged, measure the diameter and the pitch.  Your mechanic friends most certainly should be able to help.

If it is M8 X 0.75, you likely need this one.  That is the same one I use on my Nomad Mk II.
https://www.sjscycles.co.uk/bottom-brackets/thorn-m8-extra-fine-conepointed-screw-for-eccentric-bottom-bracket-shell/

One thing that has not been mentioned here, if you get them out and get new bolts, you should install the eccentric so that the thick metal part is the part that the pinch bolts press against.  If you set it up so the pinch bolts press against thin metal, it may deform, thus you want to avoid that.  See attached photo of mine, the thick part of the eccentric is on the bottom where the pinch bolts are, not the thin part of the eccentric.

Thanks a lot for all yours answers. I'll try to contact the man who sold me the bike and ask him what happened.

Some colleagues of mine are mechanic, I'll have some help of that topic.

Do you think that the threading is to be metric?

The welds holding the nuts on look to be crudely executed. It occurs to me that an alternative approach would be to carefully grind through them using a thin cutting disc and remove the nuts with the sheared setscrews in situ.  Either new stainless nuts could be welded on, with minimal damage to the paintwork, or an expanding eccentric BB shell could be fitted, if one of a suitable diameter can be sourced.

I can't imagine how the eccentric pinch bolts could shear off...

George, I wondered the same thing, so I tried to play forensic analyst...

I went to the linked profile of the frame and note Thorn is (currently) selling the frame alone and says, "These frames are made to a price, finish is not perfect but completely functional". This indicates the frames weren't made to the same spec as Thorn's higher priced offerings. The rear dropouts support this, as they differ from the other tandems Thorn produced.

In Cedric's photos, the sockets for the machine screws aren't milled from billet and circumferentially welded as on our Nomads. Rather, they are nuts tack-welded to the eccentric BB shell. I'm not sure the screws are the same diameter or fine pitch as ours. If the pitch is more coarse and the diameter smaller, then any shearing might have been the result of the previous owner's attempts to get the eccentric screws tight enough to hold against the force of two people's pedaling torque.

It is odd they'd shear at about the same point, but I suppose the nuts could have served as a collar to isolate the threaded shaft until it emerged and twisting forces concentrated on the unsupported shaft. A bit hard to tell, but I think the break doesn't look clean enough to be sawn through, and my first thought -- that they'd somehow hit something and sheared from impact -- isn't supported by the photos.

Just some thoughts on a Friday morning that saw me awakening to reddened leaves on the trees -- strong hints of Fall!

Best, Dan.

It appears the machine screws have sheared flush from the application of too much torque. If so, then a time tested means for extraction involves drilling and using a screw extractor ("EZ Out").

Best, Dan.