Paul, that engine is Model 331877, Type 0240, Trim B5. Because it is a 33 cubic inch Intek, the tappet clearances I quoted (0.003 - 0.005") are correct. The usual practice is to aim for 0.004", and that is what I suggest you do.

You lost the lottery: it is an Intek, not a Vanguard (which costs more and seems to have a substantially better reliability record). Essentially, Briggs commissioned Daihatsu to design the Vanguard with the intention of making at least the single cylinder version itself. However it found it too difficult to make and redesigned it to overcome this, renaming it Intek, while continuing to sell the Daihatsu-built twin Vanguard, and commissioning Mitsubishi to build the single Vanguard. The Mitsubishi deal quickly fell through and Briggs subsequently manufactured that engine itself. Unfortunately the Briggs redesign from Vanguard to Intek had some unfortunate effects in a couple of areas. On the single cylinder Intek, the main problem is a propensity to blow head gaskets. The twin has that problem but also had until recently a problem with the air cleaner box leaking and dusting the engine.

Here is the Illustrated Parts List for your engine:
http://bsintek.basco.com/BriggsDocumentDisplay/18kvuDXSnfBhU7y.pdf

The Briggs Operator's Manuals tend to focus on simple faults the average operator can fix personally, hence the reference to spark plug failures. Unfortunately most owners cannot distinguish between backfires (fuel explosions in the muffler) and several other faults such as spits, and in the case of LPG engines, fuel explosions in the intake manifold or air cleaner. Because you have an Intek that won't crank, the odds are rather strongly in favour of the exhaust tappet being a bit loose or the camshaft worn out (the former being much more likely). On the Intek and Vanguard engines it is essential to adjust the tappets at least once per year. If you do that, you probably won't have the failure-to-crank problem until the camshaft wears out, which is likely to be a long time.