@Janger
If you crank the thermostat to far above room temp (40C) does it function properly? Could be that you're just too close to the goal temp, so it only kicks on in short stints?
I had a similar issue, it turned out it was two part: The blower motor was weak, and the vacuum switch (shown in your second pic, top center) was tough to switch.
--> Thinking back, the issue was near identical, the furnace would kick on for a bit, then turn off, and cycle like that. In the winter my house went from room temp, down to 14C, but took a period of days to do so. Becuase it cycled on and off just enough to almost maintain temp.
As a workaround while diagnosing, I jumpered the two leads coming out of the vacuum switch once the furnace was actually on (20 second window). I used the appropriate amperage fuse to make the jump, just in case.
--> For testing, try the same, jump the vacuum switch leads at difference stages in the cycle!
----> When are you available to hangout, I could bring a fuse and try with you.
Edit: Jumper goes in to replace the vaccuum switch when there is actual fire in the furnace. If you jump it before hand, then start the furnace, it will error out that the switch is stuck. Need to start like normal, then switch when you see fire. If it stays on for a full cycle (1/2 hour or w/e) then you have found the issue!