If you've narrowed down a fault to two suspect components, the faulty one will be the one you choose not to order.
Strange intermittent fault on an Ideal Icos/Isar/Istore? Check the rear of the heat exchanger, they tend to melt and can play buggery with the wiring loom.
Ferolli Modena 102 and similar firing up for seconds at a time with NO DEMAND is caused by faulty thermistors usually. Doing the same with demand, is usually caused by the venturi failing. DO NOT REMOVE unless you are 100% sure or have a replacement, 9 times out of 10 it will turn to a little pile of dust as soon as you touch it!
Ariston Microgenus, usually give a fault code relating to the air pressure switch, most of the time its the fan. They seem to be running perfectly, but they slow down with age and don't spin fast enough to operate the APS.