I would check the hoses as others have mentioned first
Do you have access to another generator mechanic?
The generator may have been ignored in the past, but you can change the plugs, wires, ignition cap, fuel hoses. I am not a mechanic, but this sounds strange to me. The mechanics comments
You stated the impeller was replaced, were there any missing pieces? if so one thing the Westerbeke manual states is to check the heat exchanger for missing impeller pieces and remove them.
I cannot get the link to Westerbeke.com to come up to give you a link to the Operators manual for the 7.0KW BCGB - 60HZ gasoline generators single phase publication No. 44200 June 1999 1st edition
But here is what the manual suggests;
1. Faulty shutdown switch (oil pressure, water or exhaust temperature)
2. High engine or exhaust temperature
3. Dirty fuel/water separator filter.
4. Mechanical check valve at the fuel supply faulty. (If installed)
5. Low oil level in sump
f6.Faulty fuel pump
7. Faulty engine temperature sensor
Here is the link address, but getting it to come up is slow, very slow?
http://www.westerbeke.com Look under the tab labeled Parts Kits & Manuals