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What you state is essentially correct.
However a "engine laquer" is heat and oil resistant.
Remember the old school cast-iron radiators - they certainly did not slap any engine paint / machinery enamel on them.
Dulux at best Lol , the problem being that Dulux , B&Q etc. are a cheap alkyd - that colour changes depending on ambient sunlight , more likely to fade out - loose its gloss and then chalk. At that stage - it will not stand up well to heat or oil contamination.
A Litre of Tractor Enamel / Machinery enamel or Engine Enamel will cost you twice the ££ , will not have the gloss af a traditional Coach Paint (there is less varnish content) - also you would never need the possibility of a final clear over-varnish.
The additional £££ cost is because you are buying the equiv. of a automotive alkyd such as a Transport PU (more or less the same but reinforced with PU) , a transport PU would normally be used for just the cab livery because it costs so much, the rest a cheaper grade would be used. I have some wheel-sets done with both Berger & Parsons (Dagenham) Transport PU - still with a shine & no chalking - 30 yers + since painted.
The other additional feature for your money £££ , longer life, longer gloss retention , ability to withstand wash-down chemicals and abrasion, it will stand up to oil & fuel spills as well as a chassis paint (when dry through).
So - yes , depends on if it is your own vehicle or for a quick re-sale , possibly your own - you don't wish to re-paint your engine so often.