No, it wouldn’t make any difference.
you should have around 22V to 27V on the Anode Side when S1 Switch in Run/Prime Position
View attachment 901953
this would be on Terminal 5 of S5
You should have 0.5 V less on Terminal 2 and on Terminal 3 of S5
You should also have this Voltage on K8 terminals 11 and 12 and on K13 terminals 7 and 1
If you test in this sequence then you are following the exact voltage path of this circuit.
It is not uncommon that the switches, terminals, relay sockets etc are dirty, corroded or loose. The S5 switch is also suspect to wear and so is K1 itself
Just removing one wire can make or brake a circuit, which may have happened here in your case and the thing started to work again for the moment