I solved it, thanks for your help :)

The relay winding is powered directly by the mains and current can only be interrupted by the main power switch and one of the two pressure switches. As there was electrolyte in the connecting gas line when I got the device, I’m suspecting the switch is damaged and doesn’t have enough hysteresis anymore, causing the rapid switching.

• The heatsink is for a triac doing phase angle control. The second pressure switch is supposed to be set to a lower pressure and if it closes, it inhibits the phase angle control, stopping gas production. The problematic pressure switch seems to be just a redunandancy that removes power from the entire circuit using the relay.
• As I found out, “manually affecting the circuit driving the relay” is just operating the main power switch, and that works without any issues.
• There is no discrete transistor in the circuit :)

My solution was to move the set points of the two pressure switches further apart (there are screws on them for that), so the switch inhibiting the triac triggers first again.